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Preventing Concept Drift.mhtml
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From: <Saved by Blink>
Snapshot-Content-Location: https://chatgpt.com/c/6f6a86a2-0e53-410c-8ed6-3969dd8dd931
Subject: Preventing Concept Drift
Date: Mon, 1 Jul 2024 13:06:34 -0300
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class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-2" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb217da-eac2-4354-a5a3-5b7c774514f1" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>This article presents a game-learning program called TD-Gammon. TD-Gammon is a neural
network that trains itself to be an evaluation function for the game of backgammon by playing
against itself and learning from the outcome. Although TD-Gammon has greatly surpassed all
previous computer programs in its ability to play backgammon, that was not why it was developed.
Rather, its purpose was to explore some exciting new ideas and approaches to traditional problems
in the field of reinforcement learning.
The basic paradigm of reinforcement learning is as follows: The learning agent observes an input
state or input pattern, it produces an output signal (most commonly thought of as an "action" or
"control signal"), and then it receives a scalar "reward" or "reinforcement" feedback signal from the
environment indicating how good or bad its output was. The goal of learning is to generate the
optimal actions leading to maximal reward. In many cases the reward is also delayed (i.e., is given
at the end of a long sequence of inputs and outputs). In this case the learner has to solve what is
known as the "temporal credit assignment" problem (i.e., it must figure out how to apportion credit
and blame to each of the various inputs and outputs leading to the ultimate final reward signal).
The reinforcement learning paradigm has held great intuitive appeal and has attracted considerable
interest for many years because of the notion of the learner being able to learn on its own, without
the aid of an intelligent "teacher," from its own experience at attempting to perform a task. In
contrast, in the more commonly employed paradigm of supervised learning, a "teacher signal" is
required that explicitly tells the learner what the currect output is for every input pattern.
Unfortunately, despite the considerable attention that has been devoted to reinforcement learning
over many years, so far there have been few practical successes in terms of solving large-scale,
complex real-world problems. One problem has been that, in the case of reinforcement learning
with delay, the temporal credit assignment aspect of the problem has remained extremely difficult.
Another problem with many of the traditional approaches to reinforcement learning is that they
have been limited to learning either lookup tables or linear evaluation functions, neither of which
seem adequate for handling many classes of real-world problems.
However, in recent years there have been two major developments which have held out the
prospect of overcoming these traditional limitations to reinforcement learning. One of these is the
development of a wide variety of novel nonlinear function approximation schemes, such as decision
trees, localized basis functions, spline-fitting schemes and multilayer perceptrons, which appear to
be capable of learning complex nonlinear functions of their inputs.
The second development is a class of methods for approaching the temporal credit assignment
problem which have been termed by Sutton "Temporal Difference" (or simply TD) learning
methods. The basic idea of TD methods is that the learning is based on the difference between
temporally successive predictions. In other words, the goal of learning is to make the learner’s
current prediction for the current input pattern more closely match the next prediction at the next
time step. The most recent of these TD methods is an algorithm proposed in [13] for training
multilayer neural networks called TD(lambda). The precise mathematical form of the algorithm
will be discussed later. However, at this point it is worth noting two basic conceptual features of
TD(lambda). First, as with any TD method, there is a heuristic error signal defined at every time
step, based on the difference between two successive predictions, that drives the learning. Second,
given that a prediction error has been detected at a given time step, there is an exponentially
decaying feedback of the error in time, so that previous estimates for previous states are also
corrected. The time scale of the exponential decay is governed by the lambda parameter.
TD-Gammon was designed as a way to explore the capability of multilayer neural networks trained
by TD(lambda) to learn complex nonlinear functions. It was also designed to provide a detailed
comparison of the TD learning approach with the alternative approach of supervised training on a
corpus of expert-labeled exemplars. The latter methodology was used a few years ago in the
development of Neurogammon, the author’s previous neural-network backgammon program.
Neurogammon was trained by backpropagation on a data base of recorded expert games. Its input
representation included both the raw board information (number of checkers at each location), as
well as a few hand-crafted "features" that encoded important expert concepts. Neurogammon
achieved a strong intermediate level of play, which enabled it to win in convincing style the
backgammon championship at the 1989 International Computer Olympiad [14]. Thus by comparing
TD-Gammon with Neurogammon, one can get a sense of the potential of TD learning relative to the
more established approach of supervised learning.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="e4687dad-7b38-4446-b574-4d8799be5743" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>TD-Gammon is a neural network program developed for playing backgammon. Unlike previous backgammon programs, TD-Gammon doesn't just aim to excel at the game but also serves as a platform to explore innovative ideas in reinforcement learning (RL). Unlike supervised learning, where a "teacher" explicitly guides the learner's outputs, RL operates on a paradigm where a learning agent improves through trial and error. The agent observes an input, makes a decision (action), and receives feedback (reward) from the environment based on the action's effectiveness. The learning objective is to maximize this reward, often received after a series of actions, which introduces the challenge of temporal credit assignment—determining which actions contributed to the final outcome.</p><p>TD-Gammon uses Temporal Difference (TD) learning, particularly the TD(lambda) method. This method focuses on reducing the difference between consecutive predictions, refining the learner’s responses over time using an error feedback that decays exponentially. This feature enables the program to adjust not just the immediate but also past predictions, enhancing learning from sequences of actions.</p><p>The significance of TD-Gammon lies in its demonstration of how multilayer neural networks can handle complex, nonlinear functions, contrasting with traditional RL methods that are restricted to simple lookup tables or linear functions. TD-Gammon also serves as a practical test of TD learning against supervised learning methods, as exemplified by its comparison with Neurogammon, an earlier neural network backgammon program trained on expert game databases through backpropagation. TD-Gammon's success has been pivotal in illustrating the potential of advanced RL techniques to address real-world problems, despite the historical challenges faced by earlier RL approaches.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r51:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-4" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21e4b-2516-44ac-9ff4-25ed8be1f9c4" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>It's from Temporal Difference Learning and TD-Gammon
By Gerald Tesauro
This article was originally published in Communications of the ACM, March 1995 / Vol. 38, No. 3.
Copyright © 1995 by the Association for Computing Machinery. Copied with permission of the
ACM.
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This HTML version was transcribed and converted by Tom Keith.
Contents
Temporal Difference Learning and TD-Gammon
Complexity in the Game of Backgammon
TD-Gammon’s Learning Methodology -- Figure 1.
Results of Training -- Table 1, Figure 2, Table 2, Figure 3, Table 3.
Understanding the Learning Process
Absolute Accuracy vs. Relative Accuracy
Stochastic Environment
Learning Linear Concepts First
Conclusion
Appendix: Performance Measures
Acknowledgments
References
About the Author
Temporal Difference Learning and
TD-Gammon
By Gerald Tesauro
Ever since the days of Shannon’s proposal for a chess-playing algorithm [12] and Samuel’s
checkers-learning program [10] the domain of complex board games such as Go, chess, checkers,
Othello, and backgammon has been widely regarded as an ideal testing ground for exploring a
variety of concepts and approaches in artificial intelligence and machine learning. Such board
games offer the challenge of tremendous complexity and sophistication required to play at expert
level. At the same time, the problem inputs and performance measures are clear-cut and well
defined, and the game environment is readily automated in that it is easy to simulate the board, the
rules of legal play, and the rules regarding when the game is over and determining the outcome.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full 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fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="01778085-241b-4484-ae61-1dd2e96250b5" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The document you've shared is from Gerald Tesauro's notable work "Temporal Difference Learning and TD-Gammon," published in the <em>Communications of the ACM</em> in March 1995. This work is pivotal in the field of artificial intelligence, particularly in exploring the application of machine learning techniques to complex games like backgammon. Tesauro's TD-Gammon not only advanced the development of game-playing artificial intelligence but also provided deep insights into the capabilities of reinforcement learning (RL), particularly the temporal difference (TD) methods.</p><p>In this paper, Tesauro discusses the evolution of machine learning within the context of board games, which have long served as excellent models for developing and testing AI algorithms due to their complexity and the clarity of their rules and objectives. The focus on TD-Gammon is significant as it highlights how neural networks can learn complex strategies in such games through the process of self-play and without explicit programming of game strategies. TD-Gammon uses the TD(lambda) algorithm, a method that enables efficient learning by leveraging differences between successive predictions to correct and improve the model iteratively.</p><p>The document also underscores the historical importance of board games in AI research, mentioning earlier milestones like Shannon's theoretical chess algorithm and Samuel's checkers program. These examples illustrate the trajectory of thought in AI, showing a shift from basic programmed strategies to advanced learning systems that adapt and improve autonomously. Tesauro's work with TD-Gammon thus stands as a bridge between early explorations in game-based AI and modern approaches that integrate deep learning, showcasing significant advancements in how machines can learn from and adapt to complex environments.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 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11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-6" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21933-b3f7-486a-ab81-46a3a6ffd4d4" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>It sounds kind of like a generative adversarial network</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-7" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 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6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="eee2866c-366c-4fcc-85bb-b936c8c333a6" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>TD-Gammon and generative adversarial networks (GANs) share some conceptual similarities but function quite differently in practice.</p><p><strong>TD-Gammon</strong> uses a reinforcement learning (RL) approach, specifically a temporal difference (TD) method. In this setup, the system learns optimal behaviors by playing against itself, continuously updating its strategy based on the outcome of each game. The learning process is driven by the goal of maximizing rewards, which, in the case of backgammon, could be winning the game or optimizing specific strategic moves. The neural network in TD-Gammon adjusts its weights based on the error in prediction of the game's outcome, learning over time to predict more accurately based on the difference between successive game states and the eventual outcomes.</p><p><strong>Generative Adversarial Networks (GANs)</strong>, on the other hand, involve two neural networks: a generator and a discriminator. The generator creates outputs (like images) that try to mimic the true data distribution, while the discriminator evaluates them against real data, aiming to distinguish genuine examples from fakes. Through their adversarial process, both networks iteratively improve—the generator producing increasingly realistic data, and the discriminator getting better at detecting fakes. This setup is akin to a constant game where each player learns to improve their strategy based on the other’s actions.</p><p>While both systems learn through a form of feedback and adaptation, TD-Gammon is focused on optimizing decision-making in a structured game environment, using the outcomes of those decisions to guide learning. GANs, however, are about creating new data instances that are indistinguishable from real ones, essentially learning the underlying distribution of data through competition between the two networks.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r5f:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-8" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb2110b-4a4b-4296-bdb6-9a994f920578" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>TD-Gammon’s Learning Methodology
We now present a brief summary of the TD backgammon learning system. For more details, the
reader is referred to [15]. At the heart of TD-Gammon is a neural network, illustrated in Figure 1,
that is organized in a standard multilayer perception (MLP) architecture. The MLP architecture,
also used in the widely known backpropagation algorithm for supervised training [9] may be
conveniently thought of as a generic nonlinear function approximator. Its output is computed by a
feed-forward flow of activation from the input nodes to the output nodes, passing through one or
more layers of internal nodes called "hidden" nodes. Each of the connections in the network is
parameterized by a real valued "weight." Each of the nodes in the network outputs a real number
equal to a weighted linear sum of inputs feeding into it, followed by a nonlinear sigmoidal
"squashing" operation that maps the total summed input into the unit interval.
The nonlinearity of the squashing function enables the neural network to compute nonlinear
functions of its input, and the precise function implemented depends on the values of the weights.
In both theory and in practice, MLPs have been found to have extremely robust function
approximation capabilities. In fact, theorists have proven that, given sufficient hidden units, the
MLP architecture is capable of approximating any nonlinear function to arbitrary accuracy [5].
The process of "learning" in an MLP consists of applying a formula for changing the weights so
that the function implemented by the network more closely approximates a desired target function.
For large networks with thousands of connections, it is generally not feasible to find the globally
optimal set of weights that gives the best possible approximation. Nevertheless, there are many
reasonably efficient learning rules, such as backpropagation, that can find a locally optimal set of
weight values. Such locally optimal solutions are often satisfactory for many classes of real-world
applications.
The training procedure for TD-Gammon is as follows: the network observes a sequence of board
positions starting at the opening position and ending in a terminal position characterized by one side
having removed all its checkers. The board positions are fed as input vectors x[1], x[2], . . . , x[f] to
the neural network, encoded using a representation scheme that is described later. (Each time step
in the sequence corresponds to a move made by one side, i.e., a "ply" or a "half-move" in
game-playing terminology.) For each input pattern x[t] there is a neural network output vector Y[t]
indicating the neural network’s estimate of expected outcome for pattern x[t]. (For this system, Y[t]
is a four component vector corresponding to the four possible outcomes of either White or Black
winning either a normal win or a gammon. Due to the extreme rarity of occurrence, triple-value
backgammons were not represented.) At each time step, the TD(lambda) algorithm is applied to
change the network’s weights. The formula for the weight change is as follows:
where alpha is a small constant (commonly thought of as a "learning rate" parameter, w is the
vector of weights that parameterizes the network, and is the gradient of network output with
respect to weights. (Note that the equation expresses the weight change due to a single output unit.
In cases where there are multiple output units, the total weight change is given by the sum of the
weight changes due to each individual output unit.)</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="3ad8132b-a563-4a6a-afa3-d7799741e867" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>TD-Gammon utilizes a multilayer perceptron (MLP) architecture, a type of neural network renowned for its capability to approximate complex nonlinear functions. This MLP consists of multiple layers, including input nodes, one or more layers of hidden nodes, and output nodes. Here’s how the learning methodology in TD-Gammon operates:</p><h3>Neural Network Structure</h3><ul><li><strong>Input Nodes:</strong> These receive input in the form of the board positions during a backgammon game. Each board position is converted into an input vector that describes the current game state.</li><li><strong>Hidden Nodes:</strong> These nodes allow the network to capture deeper, more complex patterns in the data, acting as the computational engine. The number of hidden nodes and their connectivity define the network’s ability to learn diverse functions.</li><li><strong>Output Nodes:</strong> In TD-Gammon, the output is a vector representing the neural network’s prediction of the game’s outcome from the current board position. This includes probabilities or scores for different possible end states, such as a win or loss for either player.</li></ul><h3>Learning Process</h3><ul><li><strong>Feedforward Operation:</strong> Activation flows from the input nodes through the hidden layers to the output nodes, with each node computing a weighted sum of its inputs followed by a nonlinear sigmoid activation function. This structure allows the MLP to create a mapping from inputs (board positions) to outputs (game outcome predictions).</li><li><strong>Backpropagation and Weight Adjustment:</strong> TD-Gammon employs the TD(lambda) algorithm, which adjusts the weights of the network based on the difference between predicted outcomes and actual game results. The weight update formula uses a gradient descent approach, where the gradient (partial derivative of the error with respect to each weight) indicates the direction and magnitude of change needed to minimize prediction errors.</li></ul><h3>Special Features of TD(lambda)</h3><ul><li><strong>Temporal Credit Assignment:</strong> TD(lambda) is particularly suited for environments like backgammon, where rewards (wins or losses) are delayed until the end of the game. The algorithm helps assign credit or blame to actions taken earlier in the game, using an exponentially decaying trace of past gradients.</li><li><strong>Learning Rate (Alpha):</strong> This parameter controls how much the weights are adjusted during each learning step. A smaller alpha leads to more gradual learning, reducing the risk of overshooting optimal weights but possibly slowing convergence.</li></ul><h3>Practical Considerations</h3><ul><li><strong>Approximating Nonlinear Functions:</strong> Theoretically, MLPs with sufficient hidden units can approximate any nonlinear function to arbitrary accuracy, a principle known as the universal approximation theorem. In practice, finding the exact number of units for optimal performance involves balancing computational efficiency with learning capability.</li><li><strong>Locally Optimal Weights:</strong> Given the vast number of potential weight configurations in large networks, finding a globally optimal set is often impractical. However, the learning methods employed, such as backpropagation combined with TD(lambda), are generally effective at finding locally optimal solutions that perform well for specific applications like game playing.</li></ul><p>TD-Gammon's approach to learning not only made it a formidable backgammon player but also demonstrated the potential of neural networks in mastering complex strategic games through self-play and incremental learning, a significant milestone in the development of intelligent systems.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r5m:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-10" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21e86-1922-4243-bc20-7a791d2fd72c" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>The quantity lambda is a heuristic parameter controlling the temporal credit assignment of how an
error detected at a given time step feeds back to correct previous estimates. When lambda = 0, no
feedback occurs beyond the current time step, while when lambda = 1, the error feeds back without
decay arbitrarily far in time. Intermediate values of lambda provide a smooth way to interpolate
between these two limiting cases.
At the end of each game, a final reward signal z (containing four components as described
previously) is given, based on the outcome of the game. The preceding equation is used to change
the weights, except that the difference (z- Y[f]) is used instead of (Y[t+1]- Y[t]).
In preliminary experiments, the input representation only encoded the raw board information (the
number of White or Black checkers at each location), and did not utilize any additional
pre-computed features relevant to good play, such as, e.g., the strength of a blockade or probability
of being hit. These experiments were completely knowledge-free in that there was no initial
knowledge built in about how to play good backgammon. In subsequent experiments, a set of
handcrafted features (the same set used by Neurogammon) was added to the representation,
resulting in higher overall performance.
During training, the neural network itself is used to select moves for both sides. At each time step
during the course of a game, the neural network scores every possible legal move. (We interpret the
network’s score as an estimate of expected outcome, or "equity" of the position. This is a natural
interpretation which is exact in cases where TD(lambda) has been proven to converge.) The move
that is selected is then the move with maximum expected outcome for the side making the move. In
other words, the neural network is learning from the results of playing against itself. This self-play
training paradigm is used even at the start of learning, when the network’s weights are random, and
hence its initial strategy is a random strategy. Initially, this methodology would appear unlikely to
produce any sensible learning, because random strategy is exceedingly bad, and because the games
end up taking an incredibly long time: with random play on both sides, games often last several
hundred or even several thousand time steps. In contrast, in normal human play games usually last
on the order of 50-60 time steps.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-11" 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relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="328cbb3c-ad33-4228-a68b-cc4ce0211284" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The description provided offers a deeper look into how TD-Gammon utilizes the temporal difference (TD) learning method, particularly focusing on the parameter <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.6944em;"></span><span class="mord mathnormal">λ</span></span></span></span> and its role in the learning process.</p><h3>The Role of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.6944em;"></span><span class="mord mathnormal">λ</span></span></span></span></h3><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.6944em;"></span><span class="mord mathnormal">λ</span></span></span></span> in TD-Gammon acts as a key parameter that manages the extent to which an error influences previous state estimations, an aspect crucial in games with delayed rewards like backgammon:</p><ul><li><strong><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\lambda = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.6944em;"></span><span class="mord mathnormal">λ</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.2778em;"></span></span><span class="base"><span class="strut" style="height: 0.6444em;"></span><span class="mord">0</span></span></span></span></strong>: The learning updates are short-sighted, meaning only the current time step's error is considered for updating weights. This setting does not consider the future consequences of actions, focusing purely on immediate outcomes.</li><li><strong><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\lambda = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.6944em;"></span><span class="mord mathnormal">λ</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.2778em;"></span></span><span class="base"><span class="strut" style="height: 0.6444em;"></span><span class="mord">1</span></span></span></span></strong>: Errors affect all previous states equally, no matter how far back in time, allowing for a long-range planning perspective. This can lead to significant changes in the policy even from distant past actions but may also introduce more variance and noise in the updates.</li><li><strong>Intermediate values of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.6944em;"></span><span class="mord mathnormal">λ</span></span></span></span></strong>: These provide a balanced approach, where the influence of an error decays exponentially over previous states. This allows the model to not only learn from the immediate results but also take into account the impact of actions over a reasonably extended sequence of moves.</li></ul><h3>Learning Methodology</h3><p>During the training:</p><ol><li><p><strong>Input Representation</strong>: Initially, the network only uses the basic information of the game's state (number and position of checkers). Later experiments incorporated additional, handcrafted features that describe strategic elements of the game, such as the strength of blockades or the probability of checkers being hit. This enhancement mimics earlier efforts like Neurogammon and significantly improves performance.</p></li><li><p><strong>Self-Play</strong>: The neural network evaluates every possible legal move from a given board position and selects the move with the highest expected outcome. This self-play is crucial as it allows the system to learn effective strategies from scratch, starting with random initial weights.</p></li><li><p><strong>Effect of Random Initial Strategy</strong>: Initially, the network's predictions and decisions are based on randomly set weights, leading to highly inefficient and lengthy games. However, even from these inefficient beginnings, the network begins to discern effective strategies through continuous self-play and learning updates.</p></li></ol><h3>Practical Outcomes</h3><p>This learning setup, where the AI plays against itself with the ability to evaluate and improve its decisions iteratively, enables the network to develop sophisticated strategies without human intervention. The use of TD(<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.6944em;"></span><span class="mord mathnormal">λ</span></span></span></span>) facilitates a blend of short-term tactical and long-term strategic learning, which is pivotal in mastering a game as complex as backgammon.</p><p>TD-Gammon's methodology showcases a fundamental principle in machine learning: even from a purely exploratory start, systems can evolve to capture intricate patterns and decision frameworks, especially when the learning algorithms effectively balance between immediate and delayed outcomes.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r5t:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-12" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb2143d-9de7-4567-aa45-1c72f5f08f8b" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>Machine Learning, 23, 69-i01 (1996)
© 1996 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.
Learning in the Presence of Concept Drift and
Hidden Contexts
GERHARD WIDMER gerhard @ ai.univie.ac.at
Department of Medical Cybernetics and AI, University of Vienna, and Austrian Research Instiutte for Artificial
Intelligence, Schottengasse 3, A-IOIO Vienna, Austria
MIROSLAV KUBAT mkubat @ csi.uottawa.ca
Department of Computer Science, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada
Editor: Douglas Fisher
Abstract. On-line learning in domains where the target concept depends on some hidden context poses serious
problems. A changing context can induce changes in the target concepts, producing what is known as concept
drift. We describe a family of learning algorithms that flexibly react to concept drift and can take advantage
of situations where contexts reappear. The general approach underlying all these algorithms consists of (1)
keeping only a window of currently trusted examples and hypotheses; (2) storing concept descriptions and re-
using them when a previous context re-appears; and (3) controlling both of these functions by a heuristic that
constantly monitors the system's behavior. The paper reports on experiments that test the systems' performance
under various conditions such as different levels of noise and different extent and rate of concept drift.
Keywords: Incremental concept learning, on-line learning, context dependence, concept drift, forgetting
1. Introduction
The work presented here relates to incremental or on-line concept learning, which has
recently received considerable attention among theoreticians (e.g., Angluin, 1988; Maass,
1991; Helmbold, Littlestone, & Long, 1992) as well as practitioners (e.g., Schlimmer
& Granger, 1986; Langley, Gennari, & Iba, 1987; Kilander & Jansson, 1993; Kubat,
1989, 1993; Salganicoff, 1993a; Widmer & Kubat, 1993), The principal task is to learn
a concept incrementally by processing labeled training examples one at a time. From
another point of view, the problem may be seen as minimizing the total number of
erroneous classifications in a feedback system: a stream of objects are classified, one
by one, as positive or negative instances of a concept, and immediately afterwards the
correct answer is received. The learner uses the current state of the knowledge base to
predict the class of each incoming example. A discrepancy between the prediction and
the real class value will usually trigger modifications to the knowledge base.
A difficult problem in such a learning scenario is that the concepts of interest may
depend on some hidden context. Mild weather means different things in Siberia and
in Central Africa; Beatles fans had a different idea of a fashionable haircut than the
Depeche-Mode generation. Or consider weather prediction rules, which may vary radi-
cally depending on the season. Changes in the hidden context can induce more or less Figure 1. Current and old concept descriptions and the window moving along the stream of examples.
radical changes in the target concepts, producing what is generally known as concept
drift in the literature (e.g., Schlimmer & Granger, 1986).
An example of real-world concept drift is described by Kubat (1992), where a system
was presented that learned to control the load redistribution in computer clusters: over-
loaded units should send part of their load to underloaded units in order to improve the
overall response time. The 'real' rules describing "overloadedness" would depend on
the workload profile as defined by the frequency of disk operations, CPU and memory
requirements, and the like. However, the only variables visible to the system were the
lengths of various CPU and disk queues. Thus, the workload structure was the hidden
context that determined the interpretation of the visible variables. Note that this context
varies in time and that similar contexts can reappear.
Effective learning in environments with hidden contexts and concept drift requires a
learning algorithm that can detect context changes without being explicitly informed
about them, can quickly recover from a context change and adjust its hypotheses to a
new context, and can make use of previous experience in situations where old contexts
and corresponding concepts reappear.
One possible approach is sketched in Figure 1. As the context is known to vary in
time, the learner trusts only the latest examples -- this set is referred to as the window.
Examples are added to the window as they arrive, and the oldest examples are deleted
from it. Both of these actions (addition and deletion) trigger modifications to the current
concept hypothesis to keep it consistent with the examples in the window. In the simplest
case, the window will be of fixed size, and the oldest example will be dropped whenever
a new one comes in.
To extend the basic model, assume that the learner maintains a store of concept de-
scriptions or hypotheses pertaining to previously encountered contexts. This is indicated
CONCEPT DRIFT AND HIDDEN CONTEXTS 71
by the boxes in the lower left part of Figure 1. When the learner suspects a context
change, it will examine the potential of the previously stored descriptions to provide bet-
ter classifications. Based on the result, the system may either replace the current concept
description with the best of the stored descriptions, or start developing an entirely new
description.
Generally, a learning algorithm embodying these ideas needs (1) operators that modify
the concept description in reaction to changes in the contents of the window; (2) the
ability to decide when and how many old examples should be deleted from the window
('forgotten'); and (3) a strategy that maintains the store of current and old descriptions
and assesses the relative merits of concept hypotheses. Clearly, items (2) and (3) will
require the system to make some guesses as to when a context change is occurring.
The basic approach to learning and forgetting will be elaborated in the following
section, where we specify a simple algorithm for maintaining a consistent concept hy-
pothesis. Section 3 looks at computational learning theory for some hints concerning the
main parameter of this algorithm (the window size). The following sections then describe
three extensions of the basic method and their realization in experimental systems: the
algorithm FLORA2 (Section 4) possesses the ability to dynamically adjust the window
to an appropriate size during learning; FLORA3 (Section 5) stores concepts for later use
and reassesses their utility when a context change is perceived; and FLORA4 (Section 6)
is designed to be particularly robust with respect to noise in the input data. Experiments
with all three algorithms under varying conditions are presented in Section 7. Finally,
Section 8 relates the FLORA approach to other research in machine learning.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-13" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="9c4a26f3-4fa3-4ce9-b574-d3235838d9d5" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The excerpt from the article by Gerhard Widmer and Miroslav Kubat discusses challenges and strategies in machine learning environments characterized by concept drift and hidden contexts. Concept drift refers to the phenomenon where the underlying rules or concepts that a model has learned change over time, often due to evolving real-world conditions. Hidden contexts are variables or conditions not directly observable by the system but significantly affect the system's performance and accuracy.</p><h3>Key Points from the Article</h3><ol><li><p><strong>Incremental or Online Learning:</strong></p><ul><li>This involves processing labeled training examples one at a time and immediately receiving feedback on the classification's accuracy.</li><li>The learning process dynamically updates the knowledge base to minimize classification errors.</li></ul></li><li><p><strong>Challenges with Hidden Contexts and Concept Drift:</strong></p><ul><li>Real-world examples include weather predictions that vary with the season or operational rules in computer systems that shift with workload profiles.</li><li>These changes require that a learning system not only detect when a context has shifted but also adapt to new rules without explicit external inputs about these changes.</li></ul></li><li><p><strong>Learning Algorithm Strategy:</strong></p><ul><li><strong>Window of Current Trust:</strong> The system maintains a 'window' of the most recent examples it trusts for making predictions. Older examples are periodically removed to keep the window up-to-date with the most relevant data.</li><li><strong>Storing and Reusing Concept Descriptions:</strong> When similar conditions or contexts reappear, the system can retrieve and reuse previous concept descriptions, potentially accelerating the adaptation process.</li><li><strong>Heuristic Monitoring:</strong> The system continuously evaluates its performance to determine when context changes might have occurred, adjusting its learning and prediction strategies accordingly.</li></ul></li><li><p><strong>FLORA Algorithms:</strong></p><ul><li>The article describes several versions of the FLORA algorithm, which progressively incorporate more sophisticated features to handle concept drift and hidden contexts:<ul><li><strong>FLORA2:</strong> Adjusts the window size dynamically based on detected changes in concept or context.</li><li><strong>FLORA3:</strong> Maintains a library of old concept descriptions and reassesses their utility when changes are suspected.</li><li><strong>FLORA4:</strong> Enhances robustness against noisy data, helping maintain accuracy despite misleading or confusing input.</li></ul></li></ul></li><li><p><strong>Experimental Evaluation:</strong></p><ul><li>The performance of these algorithms is tested under various conditions, including different levels of noise and rates of concept drift, to validate their effectiveness in real-world scenarios.</li></ul></li></ol><h3>Implications for Machine Learning</h3><p>Understanding and addressing concept drift and hidden contexts are critical for the reliability and accuracy of machine learning systems, especially in dynamic environments where conditions frequently change. The strategies discussed in this paper, particularly the use of a sliding window of recent data and the ability to recall and apply past learning, are practical solutions to these challenges. These approaches help ensure that a learning system remains relevant and accurate over time, adapting to new conditions without human intervention. This is particularly valuable in applications like predictive maintenance, financial forecasting, and adaptive control systems, where the environment and underlying data patterns are continuously evolving.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r64:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-14" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb210dc-0196-455a-95f4-2446d9b9a2a0" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>Learning and Forgetting: The General FLORA Framework
Currently, our algorithms are restricted to the relatively simple representation language
based on attribute-value logic without negation. Throughout the paper we will often use
the notion of a description item, which is a conjunction of attribute-value pairs. We will
say that a description item matches an example if it is true for it. For instance, (color - white) /~ (temperature = low) matches 'snow' and (shape : cube) does not
match the Globe. Formally, a description item matches the description of an object if all
its literals (attribute-value pairs) occur in the object's description.
In the FLORA framework, a concept description or hypothesis is represented in the
form of three description sets: the set ADES (Accepted DEScriptors) contains description
items matching only positive examples. Like the other two sets, ADES can be interpreted
as a disjunctive normal form (DNF) formula. The set NDES (Negative DEScriptors)
similarly summarizes the negative examples; and PDES (Potential DEScriptors) contains
description items that are too general, matching positive examples, but also some negative
ones. 1 The set ADES, representing the current (positive) concept hypothesis, is used to
classify new incoming examples. NDES summarizes the negative examples and is used
to prevent over-generalization of ADES (see below), while PDES acts as a reservoir of
hypotheses that are currently too general but might become relevant in the future.
Assume the following structure:
72 G. WIDMER AND M. KUBAT
ADES = {ADesl/AP1,ADes2/AP2,...}
PDES = {PDesl/PP1/PN1,...}
NDES = {NDesl/NN1,...}
where ADesi, PDesi, and NDesi are conjunctive description items; APi and PP~
are counters that specify how many positive examples in the current window match the
individual description items in ADES and PDES respectively; similarly, PNi and NNi
count how many negative examples match the respective description items. The counters
are updated with any addition to or deletion from the window and are used to decide
when to move an item from one set to another or when to drop it altogether from the
hypotheses. In any case, items are retained only if they cover at least one (positive or
negative) example in the current window.
The description items in ADES and NDES are generated by incremental generalization
in response to positive and negative instances. When new instances are added to or
deleted from the window, some items will be moved from one set to another. In particular,
the set PDES of 'potential hypotheses' contains items that were once in ADES or NDES,
but are contradicted by some examples. They are kept in PDES in the hope that they
may become relevant again when old instances are dropped from the window. More
precisely, modifications to the window can affect the contents of the description sets in
the following ways:
Adding a positive example to the window may cause a new description item to be
included in ADES, or some existing items to be either 'confirmed' or generalized to
accommodate the new instance, and/or existing items to be transferred from NDES
to PDES.
Similarly, adding a negative example to the window may cause a new description
item to be included in NDES, or some existing items to be 'reinforced' or generalized,
or existing items to be transferred from ADES to PDES.
Forgetting an example (dropping it from the window) can cause existing description
items to be 'weakened' (i.e., the corresponding counters are decremented), or even
deleted from the current description set (if the counter drops to zero), or moved from
PDES to ADES (if the example was the only negative instance covered) or to NDES
(if the example was the only positive one).
Figure 2 helps visualize what is going on during the learning process. The arrows
indicate possible migrations of hypotheses between description sets after the arrival or
deletion of a positive (G) or negative (8) instance, respectively. The extent of these
transitions for the case of n arrivals and m deletions is quantified by Kubat (1991).</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" 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10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="daa9b39d-f565-412e-a2ab-1a2730b0b5f3" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The FLORA framework presented in the paper you described operates within the realm of incremental learning, particularly focusing on efficiently managing and adapting to concept drift by modifying concept descriptions based on the dynamics of incoming data. The use of a simple attribute-value logic without negation forms the backbone of the representation language, allowing for the creation and adjustment of hypotheses as data evolves.</p><h3>Key Components of the FLORA Framework</h3><ol><li><p><strong>Description Sets</strong>:</p><ul><li><strong>ADES (Accepted DEScriptors):</strong> This set contains description items that match only positive examples, forming the core of the positive concept hypothesis.</li><li><strong>NDES (Negative DEScriptors):</strong> This set summarizes items that correspond only to negative examples, helping to prevent the over-generalization of positive descriptors.</li><li><strong>PDES (Potential DEScriptors):</strong> Contains description items that are currently too general because they match both positive and negative examples but may be refined and become useful as conditions change.</li></ul></li><li><p><strong>Description Items and Counters</strong>:</p><ul><li>Each description item is a conjunction of attribute-value pairs.</li><li>Counters associated with each item in ADES and PDES track how many positive examples match the item, while counters in PDES and NDES track matches with negative examples.</li><li>These counters are crucial for dynamically updating which set a description item belongs to, based on the evolving data within the window.</li></ul></li><li><p><strong>Dynamic Window Management</strong>:</p><ul><li>The window represents the current subset of examples that the system trusts and uses for making predictions and updating hypotheses.</li><li>As new examples arrive, they can trigger the addition of new description items to the sets or the modification of existing items, including generalizations or transfers between sets based on their performance against these examples.</li><li>Similarly, as examples are forgotten (removed from the window), this can lead to the decrement of counters, potential deletion of description items, or their movement between sets, depending on the changing relevance of the item to the concept being learned.</li></ul></li><li><p><strong>Learning and Forgetting Process</strong>:</p><ul><li>Adding a positive example could enhance or confirm the validity of items in ADES or lead to the transfer of items from NDES to PDES if they are found too general.</li><li>Adding a negative example could strengthen or generalize items in NDES, or shift items from ADES to PDES if they no longer exclusively match positive examples.</li><li>Forgetting examples affects the hypothesis by weakening the influence of certain items (reducing their counters) and may lead to their removal from the current description sets or their transfer between sets if their exclusivity changes.</li></ul></li><li><p><strong>Hypothesis Migration</strong>:</p><ul><li>The system is designed to allow the migration of hypotheses between the three description sets based on the arrival or deletion of examples. This migration helps the system adapt to new information and discard outdated or irrelevant information, thus managing concept drift effectively.</li></ul></li></ol><p>This framework provides a robust method for handling environments where the underlying concepts change over time or are influenced by hidden contexts. By maintaining dynamic sets of descriptors and adapting these based on real-time data flow, FLORA aims to stay responsive and accurate even in shifting conditions. The method's effectiveness hinges on its ability to balance memory (retaining useful past hypotheses) and adaptability (updating or discarding hypotheses as needed).</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r6b:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-16" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21ed9-1481-4efa-b3a5-5d60f548a972" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>Artificial Intelligence
Volume 52, Issue 2, December 1991, Pages 169-182
Research note
Conceptual inductive learning: The case of unreliable teachers
Author links open overlay panelMiroslav Kubat
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https://doi.org/10.1016/0004-3702(91)90041-H
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Abstract
Various algorithms for learning from examples usually suppose more or less reliable sources of information. In this paper, we study the influence of unreliable information sources on the learning process and the recovery possibilities. The problem is analyzed within the frame of the rough set theory which seems to be a suitable means for treating incomplete and uncertain knowledge. We briefly report on the learning system FLORA which is based on this theory.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-17" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 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10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="dd400fad-1a0d-40dc-8382-d209e1b9004a" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The article from <em>Artificial Intelligence</em> journal, written by Miroslav Kubat in December 1991, addresses the challenge of conceptual inductive learning in the presence of unreliable information sources. Here's a breakdown of the key points from the article based on your description:</p><h3>Focus of the Study</h3><ul><li><strong>Unreliable Information Sources:</strong> Kubat explores how the learning process is impacted when the information provided for training machine learning algorithms is unreliable. This could include incorrect, incomplete, or inconsistent data provided by the sources.</li><li><strong>Recovery Possibilities:</strong> The study not only identifies the problems associated with unreliable information but also investigates methods for recovering from the misinformation to still achieve effective learning outcomes.</li></ul><h3>Theoretical Framework</h3><ul><li><strong>Rough Set Theory:</strong> The research utilizes rough set theory, which is well-suited for handling scenarios where knowledge is incomplete or uncertain. Rough set theory provides a mathematical framework to deal with vagueness and uncertainty in decision-making processes, making it an excellent tool for this study.</li></ul><h3>Learning System: FLORA</h3><ul><li><strong>FLORA System:</strong> Kubat briefly reports on the learning system named FLORA, which is based on rough set theory. The FLORA system likely incorporates mechanisms to handle and adapt to the unreliability of data sources by employing strategies that mitigate the effects of such deficiencies.</li></ul><h3>Implications and Applications</h3><ul><li><strong>Conceptual Inductive Learning:</strong> This type of learning involves generalizing from examples to form broader concepts or categories. The reliability of the information sources is crucial because inaccuracies can lead to incorrect or skewed concept formation.</li><li><strong>Handling Unreliable Data:</strong> The study's relevance extends to real-world applications where data reliability is often an issue, such as in sensor networks, user-generated content, or historical datasets with missing information.</li></ul><h3>Contribution to AI and Machine Learning</h3><ul><li>The research provides insights into designing learning algorithms that are robust against the quality issues of input data. This is particularly valuable for developing AI systems that operate in dynamic and uncertain environments, where data integrity cannot always be guaranteed.</li></ul><p>Kubat's work highlights the importance of considering the reliability of data in machine learning processes and developing methodologies that can effectively deal with the imperfections of real-world data. This approach not only improves the robustness of AI systems but also enhances their applicability in various complex scenarios.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r6i:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-18" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21e35-409d-4664-b36f-db83730f26d2" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>Effective Learning in Dynamic Environments
by Explicit Context Tracking
Gerhard Widmer 1 and Miroslav Kubat 2
Dept. of Medical Cybernetics and Artificial Intelligence, University of Vienna, and
Austrian Research Institute for Artificial Intelligence,
Schottengasse 3, A-1010 Vienna, Austria
e-mail: [email protected]
Institute of Biomedical Engineering, Dept. for Medical Informatics,
Graz University of Technology
Brockmanngasse 41, A-8010 Graz, Austria
e-mail: [email protected]
Abstract. Daily experience shows that in the real world, the meaning
of many concepts heavily depends on some implicit context, and changes
in that context can cause radical changes in the concepts. This paper
introduces a method for incremental concept learning in dynamic envi-
ronments where the target concepts may be context-dependent and may
change drastically over time. The method has been implemented in a
system called FLORA3. FLORA3 is very flexible in adapting to changes
in the target concepts and tracking concept drift. Moreover, by explicitly
storing old hypotheses and re-using them to bias learning in new con-
texts, it possesses the ability to utilize experience from previous learning.
This greatly increases the system's effectiveness in environments where
contexts can reoccur periodically. The paper describes the various algo-
rithms that constitute the method and reports on several experiments
that demonstrate the flexibility of FLORA3 in dynamic environments.
1 Introduction
One of the basic tasks of Machine Learning is to provide methods for deriving
descriptions of abstract concepts from their positive and negative examples. So
far, many powerful algorithms have been suggested for various types of data,
background knowledge, description languages, and some special 'complications'
such as noise or incompleteness.
However, relatively little attention has been devoted to the influence of vary-
ing contexts. Daily experience shows that in the real world, the meaning of many
concepts can heavily depend on some given context, such as season, weather, ge-
ographic coordinates, or simply the personality of the teacher. 'Ideal family' or
'affordable transportation' have different interpretations in poor countries and
in the North, the meaning of 'nice weather' varies with season, and 'appropriate
dress' depends on time of day, event, age, weather, and sex, among other things.
So time-dependent changes in the context can induce changes in the meaning or
definition of the concepts to be learned. Such changes in concept meaning are
sometimes called concepi drift (especially when they are gradual).
228
To discover concept drift, the learner needs feedback from its classification
attempts, to update the internal concept description whenever the prediction
accuracy decreases. This was the experimental setting of the system FLORA,
which was first published in Kubat (1989), with a theoretical analysis in Kubat
(1991). The system, though very simple, was successfuly applied in an expert-
system-driven control mechanism for load re-distribution in computer networks
(Kubat, 1992).
Frankly spoken, the original program FLORA was not very sophisticated
from the machine learning (ML) point of view because it did not contain such
common ML mechanisms as explicit generalization operators or search heuristics.
These came later, in the frame of FLORA2 (Widmer ~: Kubat, 1992) where some
kind of intelligence was implemented (generalization, check for subsumption, and
flexible reaction to the speed of drift).</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-19" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="56515b68-1ed1-4485-95de-86012f3cc01d" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The paper "Effective Learning in Dynamic Environments by Explicit Context Tracking" by Gerhard Widmer and Miroslav Kubat delves into the challenges and solutions for machine learning in dynamic environments where the meaning of concepts can change due to varying contexts. This work is particularly focused on the development and capabilities of the system FLORA3, which is an advancement over their previous systems like FLORA and FLORA2. Here's an outline of the key points and contributions of the paper:</p><h3>Context-Dependent Concept Learning</h3><ul><li><strong>Problem Statement:</strong> In real-world scenarios, the significance and definition of concepts can shift dramatically based on context, such as geographic location, weather conditions, and social circumstances. This phenomenon, known as concept drift, presents significant challenges for traditional machine learning systems that assume static target concepts.</li><li><strong>FLORA3's Approach:</strong> The system is designed to adapt dynamically to changes in context by monitoring the effectiveness of its concept classifications and updating its internal models accordingly. This allows FLORA3 to remain effective even as the definitions of target concepts evolve.</li></ul><h3>Methodology</h3><ul><li><strong>Incremental Learning:</strong> FLORA3 implements incremental concept learning, where it continuously updates its knowledge base with new examples and adjusts its hypotheses about the target concepts based on the feedback from classification attempts.</li><li><strong>Explicit Context Tracking:</strong> Unlike its predecessors, FLORA3 explicitly tracks changes in context and uses this information to adjust learning strategies. This involves storing hypotheses about past contexts and reusing them when similar contexts reappear, enhancing the system's ability to handle recurrent patterns in concept changes.</li></ul><h3>System Evolution and Features</h3><ul><li><strong>From FLORA to FLORA3:</strong><ul><li><strong>FLORA:</strong> Initially a simple system used in expert-system-driven mechanisms, lacking advanced machine learning techniques like generalization operators or heuristic searches.</li><li><strong>FLORA2:</strong> Introduced more sophisticated machine learning mechanisms, including generalization capabilities and the ability to handle faster rates of concept drift.</li><li><strong>FLORA3:</strong> Builds upon the previous versions by adding explicit context tracking and the ability to reuse historical data, significantly improving adaptability and predictive accuracy in dynamic environments.</li></ul></li></ul><h3>Experimental Evaluation</h3><ul><li>The paper reports on various experiments that demonstrate FLORA3’s flexibility and effectiveness in environments with frequent and significant concept drift. These experiments likely assess the system’s ability to adapt to changing contexts and maintain high levels of classification accuracy over time.</li></ul><h3>Significance and Applications</h3><ul><li><strong>Handling Dynamic Changes:</strong> FLORA3’s ability to explicitly track and adapt to context changes makes it particularly valuable for applications in areas like weather forecasting, stock market analysis, and adaptive traffic management, where conditions can change rapidly and unpredictably.</li><li><strong>Utilizing Experience from Previous Learning:</strong> By storing and reusing old hypotheses, FLORA3 effectively leverages past learning to enhance its performance in similar future situations, a feature that mimics human learning processes and offers a significant advantage over systems that do not remember past contexts.</li></ul><p>This work by Widmer and Kubat emphasizes the importance of adaptability in machine learning systems, particularly in our increasingly dynamic world where the ability to quickly adjust to new information is crucial for maintaining relevance and accuracy.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 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type="button" id="radix-:r6p:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-20" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb216ee-7403-43b0-8dba-425d4fe3118d" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>3 The basic FLORA framework: learning and forgetting
In this section we briefly review the basic learning mechanism in the FLORA
framework, as it was already realized in FLORA2 (Widmer • Kubat, 1992). The
following section will then describe the more advanced features of FLORA&
The principle of the FLORA algorithm is shown in Figure 1. The rectangle
'knowledge' stands for the current concept description, the rectangle 'window'
contains the currently trusted examples. Each time a new example arrives, it
is added to the window; from time to time, the oldest or, alternatively, least
relevant example is deleted from the window. Both events necessitate updates
to the concept description.
knowledge
context 1 I 2
\
examples (
context 2
Fig. 1. The window of the system FLORA moving across the stream of examples.
The concept description is represented by three description sets, ADES,
PDES, and NDES. The description sets are collections of description items---
conjunctions of attribute-value pairs. Thus a description set can be interpreted
as a DNF expression. ADES is a set of 'accepted' description items (D/s) cov-
ering only positive examples in the window (not necessarily all of them) and
no negative examples; PDES is a set of 'potential' Dis, covering both positive
and negative examples; NDES is a set of 'negative' Dis, covering only negative
examples. Any DI for which we cannot find at least one example in the window
is deleted. (Widmer & Kubat, 1992) gives an intuitive motivation for these three
sets. Obviously, each example that is being added to or deleted from the window
may be described by a number of Dis. This entails the following consequences:
Adding a positive example to the window can cause new description items to
be included in ADES, or some existing items to be 'confirmed,' or existing items
to be transferred from NDES to PDES.
231
Adding a negative example to the window can cause new description items
to be included in NDES, or some existing items to be 'reinforced,' or existing
items to be transferred from ADES to PDES.
Forgetting an example can cause existing description items to be 'weakened,'
or even deleted from the current description set, or moved from PDES to ADES
(if the example was negative) or to NDES (if the example was positive).
Figure 2 summarizes these updates. The arrows indicate possible migrations
of description items between sets after learning (L) or forgetting (F) from a
positive (+) or negative (-) instance, respectively.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-21" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="1b4b4db6-92ad-4dbf-ac96-1b214608ad95" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The FLORA framework, particularly in its FLORA2 implementation, employs a dynamic method for learning and forgetting in the realm of machine learning. This system focuses on adapting concept descriptions based on the continuous flow of incoming examples, each labeled as either positive or negative. Below is a summary of the mechanisms described in the FLORA2 framework:</p><h3>Core Components of FLORA2</h3><ol><li><p><strong>Knowledge and Window:</strong></p><ul><li><strong>Knowledge</strong>: Represents the current concept description, maintained by the system.</li><li><strong>Window</strong>: Contains the set of examples currently trusted by the system. This window adjusts dynamically by adding new examples and removing old or less relevant ones.</li></ul></li><li><p><strong>Description Sets:</strong></p><ul><li><strong>ADES (Accepted Description Items)</strong>: This set includes description items that cover only positive examples from the window, with no negative examples included.</li><li><strong>PDES (Potential Description Items)</strong>: Includes items that cover both positive and negative examples, indicating their potential relevance but not yet confirmed for specificity.</li><li><strong>NDES (Negative Description Items)</strong>: Contains items that exclusively cover negative examples, helping to differentiate what the concept is not.</li></ul></li></ol><h3>Learning and Forgetting Mechanisms</h3><ul><li><p><strong>Adding Examples</strong>:</p><ul><li>When a new <strong>positive example</strong> is added, it may:<ul><li>Lead to the inclusion of new description items in ADES.</li><li>Confirm existing items in ADES.</li><li>Transfer items from NDES to PDES if they are now seen as potentially applicable to positive examples.</li></ul></li><li>When a new <strong>negative example</strong> is added, it may:<ul><li>Result in new items being added to NDES.</li><li>Strengthen existing items in NDES.</li><li>Transfer items from ADES to PDES, indicating their potential but non-exclusive negative application.</li></ul></li></ul></li><li><p><strong>Forgetting Examples</strong>:</p><ul><li>Removing an example can lead to:<ul><li>Existing description items being weakened or deleted if they no longer find support in the window.</li><li>Movement of items from PDES to ADES if the forgotten example was a negative one, suggesting the item may now be more indicative of a positive concept.</li><li>Transfer of items from PDES to NDES if the forgotten example was positive, suggesting the item is more indicative of a negative concept.</li></ul></li></ul></li></ul><h3>Visualizing Updates</h3><p>The process of learning (L) and forgetting (F) is visualized through diagrams where arrows show possible migrations of description items between the different sets, depending on whether the learning or forgetting involved a positive (+) or negative (-) example.</p><h3>Significance of FLORA2</h3><p>FLORA2's methodological approach to learning and forgetting allows it to adaptively manage concept drift by continuously updating its concept descriptions based on the most recent and relevant examples. This dynamic approach is particularly valuable in environments where the relevance of concepts may change over time, requiring the system to both learn new patterns and unlearn outdated or incorrect information effectively.</p><p>This framework ensures that the system remains efficient in its classifications by maintaining a balance between stability and plasticity, allowing it to respond flexibly to new information while retaining valuable learned knowledge from past examples.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r70:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-22" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb2152d-b830-4dfe-97a8-1985c1e5dccf" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>4.2 Storage and re-use of old contexts
As already noted, there are many natural domains where there is a finite num-
ber of hidden contexts that may reappear, either cyclically or in an unordered
235
fashion. In such domains, it would be a waste of effort to re-learn an old concept
from scratch when it reappears. Instead, concepts or hypotheses should be saved
so that they can be re-examined at some later time, when there are indications
that they might be relevant again. The effect should be faster convergence if the
concept (or some similar one) has already occurred. FLORA3 includes a mech-
anism for doing just this. In designing this mechanism, several questions had to
be answered:
1) Which parts of a hypothesis should be stored?
2) Which hypotheses are worth saving?
3) When should old hypotheses/concepts be reconsidered?
4) How can the adequacy or 'degree of fit' of an old concept be measured in a
new situation?
5) How is an old hypothesis/concept to be used in a new situation?
The answer to question 1) is quite simple: the concept description/hypothesis
is a triple {ADES, PDES, NDES} and is saved as such, because these sets sum-
marize the current state of affairs. The match counts associated with the de-
scription items in the sets are not stored, because they will not be meaningful
in some new situation.
In designing a solution to question 5), we note that when an old concept
is retrieved at some later point in time, it finds itself in a new context: it will
not agree with all the training instances in the current window; some items in
the concept's description sets will be too specific, and others will be inconsistent
with the data. Thus, it is not enough just to recompute the counts for the various
description items. Instead, all the instances in the current window must be re-
generalized. The retrieved concept is used as a model in this re-generalization
process: the counts associated with all the items in the description sets are set
to zero, and then the regular FLORA learning algorithm is invoked for every
training instance in the current window. Instances that fit items already in the
concept's description sets will confirm these items, and generally, those partial
generalizations in the old concept that are in accordance with the new data will
be used in the re-generalization process. Others will not be confirmed by the
new instances and thus their counts will remain at zero. After re-generalizing
all instances in the window, all those description items that still have counts of
zero are removed as incorrect or irrelevant from the updated concept.
As for questions 2)- 4) -- which hypotheses deserve to be saved, and when;
when should old concepts be reconsidered; how is the appropriateness of an
old concept to a new situation measured -- the criteria that can be used to
make these decisions can only be of a heuristic nature. Intuitively, only stable
hypotheses/concepts should be saved, and the system should reconsider some
old concepts whenever it perceives some substantial concept drift. It is the win-
dow adjustment heuristic (WAH) that tries to determine precisely these circum-
stances. So in FLORA3, storage and re-examination of old hypotheses are tightly
linked to changes in the window size.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-23" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 25.8215 3.85078C24.8796 2.7893 23.7219 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11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="1a12912b-7901-4c14-996b-556049ebd811" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The section on "Storage and re-use of old contexts" in FLORA3 addresses a key challenge in dynamic learning environments: efficiently recalling and applying previously learned concepts when similar contexts or situations reoccur. Here's a detailed breakdown of how FLORA3 handles this process:</p><h3>1. <strong>Storing Old Hypotheses</strong></h3><ul><li><strong>What to Store:</strong> FLORA3 stores the concept description as a set of three components: ADES (Accepted Description Items), PDES (Potential Description Items), and NDES (Negative Description Items). These sets summarize the concept at the time of storage. Notably, the match counts that specify how often items matched instances are not saved because their relevance might not persist in new contexts.</li></ul><h3>2. <strong>Re-using Old Hypotheses</strong></h3><ul><li><strong>Reconsideration of Hypotheses:</strong> When an old concept is brought back into consideration, it must be adapted to fit the new context. This involves resetting the counts of description items to zero and re-generalizing based on the current examples in the window. This process ensures that only those parts of the old concept that still align with the current data are retained.</li><li><strong>Process of Re-generalization:</strong> Each training instance in the current window is used to re-validate or reject the old concept's description items. Those that no longer match any instances are removed, ensuring the concept remains relevant and accurate.</li></ul><h3>3. <strong>Heuristic Decisions for Managing Hypotheses</strong></h3><ul><li><strong>Determining What to Save:</strong> Not all hypotheses are worth saving. FLORA3 focuses on storing stable, frequently useful concepts that have proven their value in past situations.</li><li><strong>Deciding When to Reconsider Old Concepts:</strong> The system re-examines old hypotheses when significant concept drift is detected, suggesting that a previously encountered situation might be relevant again.</li><li><strong>Evaluating the Fit of Old Concepts:</strong> The appropriateness of an old concept in a new situation is assessed through a heuristic process, part of the window adjustment heuristic (WAH), which analyzes changes in context and the window of current examples to decide if an old hypothesis might be applicable.</li></ul><h3>4. <strong>Integration with Learning Algorithm</strong></h3><ul><li>The re-use of old concepts is deeply integrated with the regular learning processes of FLORA3. When an old hypothesis is reconsidered, it is not simply reinstated but is actively re-evaluated and re-adjusted to ensure that it accurately reflects the new data and conditions. This integration helps maintain the system's flexibility and responsiveness to changing environments.</li></ul><h3>5. <strong>Practical Implications</strong></h3><ul><li><strong>Efficiency:</strong> By storing and re-using old hypotheses, FLORA3 can rapidly converge to effective solutions when familiar contexts arise, significantly reducing the learning time and computational resources required.</li><li><strong>Adaptability:</strong> This approach allows FLORA3 to remain adaptable and effective in environments where contexts and concept definitions frequently change, making it particularly valuable for applications such as weather forecasting, stock market analysis, and other areas where patterns may repeat over time.</li></ul><p>This strategy enhances FLORA3’s ability to function effectively in dynamic settings by leveraging historical data and past learning experiences, thus providing a robust method for dealing with concept drift and the cyclic reoccurrence of contexts.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" 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class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-24" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21a21-502e-405d-8717-dcf62495d1ec" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>The complete algorithm for handling old contexts works as follows:
236 - When the current concept is stable (according to the WAH- see section 4.1):
save the current hypothesis (unless there is already a stored concept with
the same set of ADES descriptions). - When FLORA3 suspects a concept drift, i.e., when the WAH enforces a
narrowing of the window: reconsider old, saved concepts and compare them
to the current hypothesis. This is done in three steps:
1) Find the best candidate among the stored concepts: an old concept be-
comes a candidate if it is consistent with the current example. All the
candidates are evaluated with respect to the ratio of the numbers of pos-
itive and negative instances that they match (from the current window).
The best candidate according to this measure is chosen.
2) Update the best candidate w.r.t, the current data: the retrieved concept
description is updated by setting all the counts in the description sets
to 0 and then re-processing all the instances in the window according to
this hypothesis (see the above discussion).
3) Compare the updated best candidate to the current hypothesis: use some
'measure of fit' to decide whether the updated candidate (= old concept)
is better than the current hypothesis; if so, replace the current hypothesis
with the updated old concept. In the current version of FLORA3, the
measure of fit is simply the relative complexity of the description, as it is
used also in the window adjustment heuristic: a hypothesis is considered
better if its ADES set is more concise. (Remember that ADES covers all
positive and no negative instances, so the number of instances covered
is the same for the ADES sets in both the current hypothesis and the
updated best candidate.)
As one possible class of application domains for the FLORA systems is flex-
ible control in real time systems (cf. Kubat, 1992), efficiency of the learning
algorithm is an important criterion. The above algorithm tries to maintain ef-
ficiency by limiting the number of expensive re-processing episodes. First, old
concepts are not reconsidered after every new training instance; they are only
retrieved when the window adjustment heuristic suspects that a concept drift is
taking place. And second, the expensive part of reconsidering an old concept--
the re-generalization of all the instances in the window--is done only for one of
them- the best candidate. Which old concept is the best candidate is deter-
mined through a simple heuristic measure, the number of positive and negative
matches (see above). This is a very weak measure, of course, and can sometimes
lead to an inappropriate candidate being chosen. Thus, efficiency is achieved at
the possible expense of quality.
It seems worth pointing out once more exactly what the role of old con-
cepts/hypotheses is in this process: at the time of a suspected concept shift, an
old concept is used to bias the re-generalization of the examples in the window.
It is not just retrieved and used as the current concept hypothesis. Instead, the
old concept is used as a model for the re-generalization of the instances: it simply
provides a list of generalizations that were useful in the past and that might, at
least in part, also be useful in the new context. This reflects the insight that when
237
an old hidden context reappears, the target concepts will tend to be similar, but
not necessarily identical to how they appeared in the old context. 3</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-25" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="22b245bf-84a0-49fc-bca8-2df6595abb49" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The algorithm detailed in the discussion for handling old contexts within the FLORA3 system is designed to efficiently manage concept drift, leveraging historical data to enhance learning accuracy without compromising the system's efficiency. Here’s a step-by-step breakdown of how the complete algorithm operates:</p><h3>1. <strong>Saving Current Hypotheses</strong></h3><ul><li><strong>Stability Check:</strong> When the current concept is deemed stable by the Window Adjustment Heuristic (WAH), the current hypothesis is saved for potential future use.</li><li><strong>Uniqueness:</strong> The hypothesis is saved only if there isn't already a stored concept with the same set of ADES descriptions, ensuring no redundant data storage.</li></ul><h3>2. <strong>Handling Suspected Concept Drift</strong></h3><ul><li><strong>Trigger:</strong> When the WAH detects a possible concept drift, indicated by a need to narrow the window of current trusted examples, the system begins to reconsider previously saved hypotheses.</li><li><strong>Steps to Reconsider Old Hypotheses:</strong><ul><li><strong>Step 1: Identifying Candidates:</strong> The system scans through stored concepts to find ones that match the current examples. Candidates are evaluated based on how well their historical data (the ratio of positive to negative instances they match from the current window) aligns with the present scenario.</li><li><strong>Step 2: Updating the Best Candidate:</strong> The selected best candidate's description is reset (all counts set to zero) and updated by re-evaluating all current window instances against this old but potentially relevant hypothesis.</li><li><strong>Step 3: Comparing and Deciding:</strong> The updated candidate is compared against the current hypothesis using a 'measure of fit'. This measure is typically the simplicity or conciseness of the ADES set. If the old concept proves a better fit—simpler and still accurate—it replaces the current hypothesis.</li></ul></li></ul><h3>3. <strong>Efficiency and Quality Trade-offs</strong></h3><ul><li><strong>Selective Reconsideration:</strong> Old concepts are not revisited after each new training instance; they're only considered when there's a suspected shift in concept, based on the window adjustment heuristic. This limits computational expense.</li><li><strong>Single Candidate Update:</strong> Only the best candidate undergoes the intensive re-generalization process, maintaining operational efficiency by avoiding exhaustive re-evaluation of all stored hypotheses.</li><li><strong>Quality Concerns:</strong> The heuristic used to select the best candidate, while efficient, is acknowledged as potentially weak, meaning it may sometimes select an inappropriate candidate, sacrificing some quality for efficiency.</li></ul><h3>4. <strong>Role of Old Hypotheses</strong></h3><ul><li><strong>Biasing Re-generalization:</strong> An old concept, when retrieved, isn't directly used as the new hypothesis. Instead, it serves as a model to guide the re-generalization process. This approach acknowledges that while the same hidden contexts might recur, the exact manifestations of the associated concepts might differ slightly from their past appearances.</li></ul><h3>Application Context</h3><ul><li><strong>Real-Time Systems:</strong> Given that FLORA systems are designed for real-time applications like flexible control systems, the efficiency of this learning algorithm is crucial. The method balances responsiveness to changing data with computational practicality, making it suitable for environments where quick adaptation is necessary but resources are constrained.</li></ul><p>This sophisticated method for revisiting and utilizing old hypotheses allows FLORA3 to dynamically adapt to new data while drawing on valuable historical insights, thus enhancing its capability to handle complex and changing environments effectively.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 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1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 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dark:bg-token-main-surface-secondary"><div>A list of all of the topics we've discussed.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full 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fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="b9e24397-4675-4d00-904a-67907551693e" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Here’s a list of the topics we've discussed:</p><ol><li><p><strong>TD-Gammon and Reinforcement Learning</strong></p><ul><li>Overview and objectives of TD-Gammon.</li><li>Differences between TD-Gammon and generative adversarial networks (GANs).</li></ul></li><li><p><strong>Gerald Tesauro’s Work on TD-Gammon</strong></p><ul><li>Description of TD-Gammon’s learning methodology from Gerald Tesauro's paper.</li><li>Comparison of reinforcement learning to traditional learning methods.</li></ul></li><li><p><strong>Concept Drift in Machine Learning</strong></p><ul><li>Exploration of concept drift and hidden contexts in machine learning, referencing Gerhard Widmer and Miroslav Kubat's work.</li><li>FLORA’s approach to learning in dynamic environments with concept drift and hidden contexts.</li></ul></li><li><p><strong>Storage and Re-use of Old Contexts in FLORA3</strong></p><ul><li>Strategies for storing and re-utilizing old contexts and hypotheses in FLORA3.</li><li>Detailed explanation of the algorithm for handling old contexts within FLORA3.</li></ul></li><li><p><strong>FLORA Framework’s Basic Mechanisms</strong></p><ul><li>Description of the basic learning and forgetting mechanisms in the FLORA framework.</li><li>Dynamics of the description sets (ADES, PDES, NDES) used in FLORA.</li></ul></li></ol><p>Each topic includes in-depth discussions on various aspects of machine learning, particularly focusing on dynamic environments, concept drift, and reinforcement learning techniques like those used in TD-Gammon.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 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text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21ff5-dd76-4bf7-8c25-58fade092d82" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>Connections with the following: RELIABLEADVERSARIALDISTILLATION
WITHUNRELIABLETEACHERS
Jianing Zhu1Jiangchao Yao2Bo Han1,†Jingfeng Zhang3
Tongliang Liu4Gang Niu3Jingren Zhou2Jianliang Xu1Hongxia Yang2
1Hong Kong Baptist University2Alibaba Group
3RIKEN Center for Advanced Intelligence Project4The University of Sydney
{csjnzhu, bhanml, xujl}@comp.hkbu.edu.hk
{jiangchao.yjc, jingren.zhou, yang.yhx}@alibaba-inc.com
ABSTRACT
In ordinary distillation, student networks are trained with soft labels (SLs) given by
pretrained teacher networks, and students are expected to improve upon teachers
since SLs are stronger supervision than the original hard labels. However, when
considering adversarial robustness, teachers may become unreliable and adversar-
ial distillation may not work: teachers are pretrained on their own adversarial data,
and it is too demanding to require that teachers are also good at every adversarial
data queried by students. Therefore, in this paper, we propose reliable introspective
adversarial distillation (IAD) where students partially instead of fully trust their
teachers. Specif i cally, IAD distinguishes between three cases given a query of a
natural data (ND) and the corresponding adversarial data (AD): (a) if a teacher is
good at AD, its SL is fully trusted; (b) if a teacher is good at ND but not AD, its SL
is partially trusted and the student also takes its own SL into account; (c) otherwise,
the student only relies on its own SL. Experiments demonstrate the effectiveness of
IAD for improving upon teachers in terms of adversarial robustness.
1INTRODUCTION
Deep Neural Networks (DNNs) have shown excellent performance on a range of tasks in computer
vision (He et al., 2016) and natural language processing (Devlin et al., 2019). Nevertheless, Szegedy
et al. (2014); Goodfellow et al. (2015) demonstrated that DNNs could be easily fooled by adding a
small number of perturbations on natural examples, which increases the concerns on the robustness
of DNNs in the trustworthy-sensitive areas, e.g., i nance (Kumar et al., 2020) and autonomous
driving (Litman, 2017). To overcome this problem, adversarial training (Goodfellow et al., 2015;
Madry et al., 2018) is proposed and has shown effectiveness to acquire the adversarially robust DNNs.
Most existing adversarial training approaches focus on learning from data directly. For example,
the popular adversarial training (AT) (Madry et al., 2018) leverages multi-step projected gradient
descent (PGD) to generate the adversarial examples and feed them into the standard training. Zhang
et al. (2019) developed TRADES on the basis of AT to balance the standard accuracy and robust
performance. Recently, there are several methods under this paradigm are developed to improve the
model robustness (Wang et al., 2019; Alayrac et al., 2019; Carmon et al., 2019; Zhang et al., 2020;
Jiang et al., 2020; Ding et al., 2020; Du et al., 2021; Zhang et al., 2021). However, directly learning
from the adversarial examples is a challenging task on the complex datasets since the loss with hard
labels is diff i cult to be optimized (Liu et al., 2020), which limits us to achieve higher robust accuracy.
To mitigate this issue, one emerging direction is distilling robustness from the adversarially pre-
trained model intermediately, which has shown promise in the recent study (Zi et al., 2021; Shu et al.,
2021). For example, Ilyas et al. (2019) used an adversarially pre-trained model to build a “robustif i ed”
dataset to learn a robust DNN. Fan et al. (2021); Salman et al. (2020) explored to boost the model
†Corresponding author ([email protected]).
1
arXiv:2106.04928v3
[cs.LG]
10
Mar
2022
Published as a conference paper at ICLR 2022
Epochs
Accuracy
of
Teacher
Model
(\%) On natural data
On student model's
adversarial data
(a) Unreliability issue
TeacherStudentItself
12
Natural data Natural data
Student
Adversarial Output Adversarial Output
Output Output
Partially Mimic
Mimic
Teacher Guidance Self-Introspection
(b) Overview of Introspective Adversarial Distillation (IAD)
Figure 1:(a) Unreliability issue: Comparison of the teacher model’s accuracy on the natural data and
the student model’s adversarial data from CIFAR-10 datasets. Different from the ordinary distillation
in which the natural data is unchanged and the teacher model has the consistent standard performance,
the teacher model’s robust accuracy on the student model’s adversarial data is decreasing during
distillation, which means the guidance of the teacher model in adversarial distillation is progressively
unreliable.(b) Overview of Introspective Adversarial Distillation (IAD): The student partially
trusts the teacher guidance and partially trusts self-introspection during adversarial distillation.
Specif i cally, the student model generates the adversarial data by itself and mimics the outputs of
the teacher model and itself partially in IAD. Note that, the concrete intuition about the student
introspection is referred to the analysis and the evidence in Figure 2 and Figure 3.
robustness through i ne-tuning or transfer learning from adversarially pre-trained models. Goldblum
et al. (2020)and Chen et al. (2021) investigated distilling the robustness from adversarially pre-trained
models, termed as adversarial distillation for simplicity, where they encouraged student models to
mimic the outputs (i.e., soft labels) of the adversarially pre-trained teachers.
However, one critical difference is: in the conventional distillation, the teacher model and the student
model share the natural training data; while in the adversarial distillation, the adversarial training
data of the student model and that of the teacher model are egocentric (respectively generated by
themselves) and becoming more adversarial challenging during training. Given this distinction, are the
soft labels acquired from the teacher model in adversarial distillation always reliable and informative
guidance? To answer this question, we take a closer look at the process of adversarial distillation. As
shown in Figure 1(a), we discover that along with the training, the teacher model progressively fails
to give a correct prediction for the adversarial data queried by the student model.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-29" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 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10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="be2a1e84-4acd-4ce2-98e0-39ef1de4fabf" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The work on "Reliable Adversarial Distillation with Unreliable Teachers" by Jianing Zhu et al. explores an advanced technique in machine learning called Introspective Adversarial Distillation (IAD), which is particularly relevant to enhancing the adversarial robustness of neural networks. Let's explore how the concepts and techniques discussed in our previous topics connect with this paper:</p><ol><li><p><strong>Adversarial Robustness and Learning from Examples</strong></p><ul><li>Like the discussions about FLORA frameworks and TD-Gammon's reinforcement learning, where the learning process adapts based on experiences and changes in environment or context, IAD also adapts based on the adversarial context presented by the environment. Both deal with dynamic, challenging environments where predefined notions or labels (whether they be the correct move in backgammon or a label provided by a teacher network in adversarial training) may not always hold true due to changing conditions.</li></ul></li><li><p><strong>Handling Unreliable Information</strong></p><ul><li>In Kubat’s discussion on learning from unreliable teachers and the adaptation of FLORA systems to manage concept drift, there is a clear parallel to managing unreliable adversarial examples in neural network training. The IAD method recognizes that adversarial examples provided by teacher networks may not always be reliable, echoing the issues discussed in the concept drift context where the relevance and accuracy of learned concepts may change over time.</li></ul></li><li><p><strong>Incremental Learning and Context Adaptation</strong></p><ul><li>FLORA systems incrementally adjust their hypotheses about concepts based on new data and old contexts, similar to how IAD adjusts its trust in the teacher's soft labels based on the context of the data (natural vs. adversarial). Both methods involve a form of re-evaluation and updating of concepts or labels in response to new information and shifted contexts.</li></ul></li><li><p><strong>Efficiency in Learning</strong></p><ul><li>Just as FLORA3 optimizes learning by selectively revisiting and utilizing old hypotheses, IAD seeks efficiency by allowing the student model to partially rely on its own generated adversarial examples alongside those provided by the teacher. This parallel use of self-guidance and external guidance helps maintain robust learning processes without excessive reliance on potentially misleading external inputs.</li></ul></li><li><p><strong>Robustness in Adversarial Environments</strong></p><ul><li>Adversarial robustness is a key theme in the IAD paper, which is fundamentally about enhancing the ability of neural networks to perform well even in the presence of intentionally misleading or challenging inputs. This goal resonates with the overarching themes in our discussions about reinforcement learning and concept drift, where the aim is to develop systems that can sustain performance and accuracy despite complex, unpredictable changes in their operating environments.</li></ul></li></ol><p>In summary, the paper by Zhu et al. on IAD extends the principles of dynamic adaptation, robustness, and efficient learning in the face of unreliable information and challenging environments, which are core themes in our discussions about machine learning in various contexts including adversarial training, concept drift, and reinforcement learning.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r7s:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-30" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21591-008d-43bc-b0e5-73fee8352359" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>2.2KNOWLEDGEDISTILLATION
The idea of distillation from other models can be dated back to (Craven & Shavlik, 1996), and
re-introduced by (Hinton et al., 2015) as knowledge distillation (KD). It has been widely studied
in recent years (Yao et al., 2021) and works well in numerous applications like model compression
and transfer learning. For adversarial defense, a few studies have explored obtaining adversarial
robust models by distillation. Papernot et al. (2016) proposed defensive distillation which utilizes the
soft labels produced by a standard pre-trained teacher model, while this method is proved to be not
resistant to the C&W attacks (Carlini & Wagner, 2017); Goldblum et al. (2020) combined AT with
KD to transfer robustness to student models, and they found that the distilled models can outperform
adversarially pre-trained teacher models of identical architecture in terms of adversarial robustness;
Chen et al. (2021) utilized distillation as a regularization for adversarial training, which employed
robust and standard pre-trained teacher models to address the robust overf i tting (Rice et al., 2020).
Nonetheless, all these related methods fully trust teacher models and do not consider that whether
the guidance of the teacher model in distillation is reliable or not. In this paper, different from the
previous studies, we i nd that the teacher model in adversarial distillation is not always trustworthy.
Formally, adversarial distillation suggests to minimizeE˜ x∈B[x][‘kl(S(˜ x|τ)||T(˜ x|τ))], whereT(˜ x|τ)
is not a constant soft supervision along with the adversarial training and affected by the adversarial
data generated by the dynamically evolved student network. Based on that, we propose reliable
IAD to encourage student models to partially instead of fully trust teacher models, which effectively
utilizes the knowledge from the adversarially pre-trained models.
3
Published as a conference paper at ICLR 2022
X1
X1’
X1’’ Student decision region
Teacher decision region
X2
(a) Toy illustration
Num
x ? 1 x ??
1 x2
Epoch
(b) Number changes on the three kinds of data during distillation
Figure 2:(a) Toy illustration: An illustration of three situations about the prediction of the teacher
model. The blue/orange areas represent the decision region (in which the model can give the correct
predictions) of the teacher/student model, and the red dashed box represents the unit-norm ball of AT.
1)x01. The generated adversarial example from the natural examplex1is located in the blue area,
where the teacher model can correctly predict; 2)x00 1. The generated adversarial example fromx1
is out of both orange and blue areas, where the teacher model has the wrong prediction; 3)x2. The
natural example that the teacher model cannot correctly predict.(b) Number changes on the three
kinds of data: We trace the number of three types of data during adversarial distillation on CIFAR-10
dataset. Noted that, different from the consistent number of examples likex2, the number of examples
like x01is decreasing and that of examples like x00 1is increasing during adversarial distillation.
3A CLOSERLOOK ATADVERSARIALDISTILLATION
In Section 3.1, we discuss the unreliable issue of adversarial distillation, i.e., the guidance of the
teacher model is progressively unreliable along with adversarial training. In Section 3.2, we partition
the training examples into three parts and analyze them part by part. Specif i cally, we expect that the
student model should partially instead of fully trust the teacher model and gradually trust itself more
along with adversarial training.
3.1FULLYTRUST: PROGRESSIVELYUNRELIABLEGUIDANCE
As aforementioned in the Introduction, previous methods (Goldblum et al., 2020; Chen et al., 2021)
fully trust the teacher model when distilling robustness from adversarially pre-trained models. Taking
Adversarial Robust Distillation (ARD) (Goldblum et al., 2020) as an example, we illustrate its
procedure in the left part of Figure 1(b): the student model generates its adversarial data and then
optimizes the prediction of them to mimic the output of the teacher model. However, although the
teacher model is well optimized on the adversarial data queried by itself, we argue that it might not
always be good at the more and more challenging adversarial data queried by the student model.
As shown in Figure 1(a), different from the ordinary distillation in which the teacher model has
the consistent standard performance on the natural data, its robust accuracy on the student model’s
adversarial data is decreasing during distillation. The guidance of the teacher model gradually fails to
give the correct output on the adversarial data queried by the student model.
3.2PARTIALLYTRUST: CONSTRUCTION OFRELIABLEGUIDANCE
The unreliable issue of the teacher model in adversarial distillation raises the challenge of how to
conduct reliable adversarial distillation with unreliable teachers? Intuitively, this requires us to
re-consider the guidance of adversarially pre-trained models along with the adversarial training. For
simplicity, we useT (x)(T (˜ x)) to represent the predicted label of the teacher model on the natural
(adversarial) examples, and useyto represent the targeted label. We partition the adversarial samples
into following parts as shown in the toy illustration (Figure 2(a)), and analyze them part by part.
1)T (x) = y ∩ T (˜ x) = y:
It can be seen in Figure 2(a) that this part of data whose adversarial
variants likex01is the most trustworthy among the three parts, since the teacher model performs well
on both natural and adversarial data. In this case, we could choose to trust the guidance of the teacher
model on this part of the data. However, as shown in Figure 2(b), we i nd that the sample number
of this part is decreasing along with the adversarial training. That is, what we can rely on from the
teacher model in adversarial distillation is progressively reduced. </div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-31" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex-shrink-0 flex flex-col relative items-end"><div><div class="pt-0.5 juice:pt-0"><div class="gizmo-bot-avatar flex h-6 w-6 items-center justify-center overflow-hidden rounded-full juice:h-8 juice:w-8"><div class="relative p-1 rounded-sm flex items-center justify-center bg-token-main-surface-primary text-token-text-primary h-8 w-8"><svg width="41" height="41" viewBox="0 0 41 41" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md" role="img"><text x="-9999" y="-9999">ChatGPT</text><path d="M37.5324 16.8707C37.9808 15.5241 38.1363 14.0974 37.9886 12.6859C37.8409 11.2744 37.3934 9.91076 36.676 8.68622C35.6126 6.83404 33.9882 5.3676 32.0373 4.4985C30.0864 3.62941 27.9098 3.40259 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10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="b77e7382-1d1f-4a8d-978b-7d00f6349bde" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The discussion of knowledge distillation (KD) in the context of adversarial robustness highlights several key points and concerns, connecting it back to broader themes we've discussed in machine learning, particularly those concerning reliability and adaptation in dynamic and challenging environments.</p><h3><strong>Connection to Previous Discussions</strong></h3><ol><li><p><strong>Adversarial Robustness and Knowledge Distillation:</strong></p><ul><li>Knowledge distillation has been applied to improve model performance and efficiency, similar to how FLORA and TD-Gammon adapt and learn. The application of KD in adversarial settings, as discussed, aims to transfer robustness from a teacher to a student model. This mirrors discussions around adaptive learning where models adjust based on the reliability of their 'teachers' or data.</li></ul></li><li><p><strong>Challenges with Unreliable Teachers:</strong></p><ul><li>Similar to the issues addressed in FLORA's handling of concept drift and the reliability of teachers discussed by Kubat, adversarial distillation faces the challenge of the teacher's guidance becoming less reliable over time. This problem necessitates a system where the student model does not fully rely on the teacher but also incorporates its own insights, akin to FLORA systems leveraging past hypotheses to adapt to new data contexts.</li></ul></li><li><p><strong>Dynamic and Incremental Learning:</strong></p><ul><li>The idea that the student model in adversarial distillation should become increasingly self-reliant reflects discussions on incremental learning and self-adjustment in response to new information. This approach is necessary in environments where the data or conditions under which the model operates are constantly changing.</li></ul></li><li><p><strong>Efficiency and Reliability in Learning:</strong></p><ul><li>The need for efficient learning strategies that do not compromise the model's performance is a common theme. In adversarial distillation, focusing only on the most reliable aspects of the teacher’s input and gradually incorporating more self-guided learning is an approach aimed at maintaining both efficiency and reliability—similar to how FLORA manages learning and forgetting by selectively revisiting old hypotheses.</li></ul></li></ol><h3><strong>Specific Insights from Adversarial Distillation</strong></h3><ol><li><p><strong>Handling Decreasing Reliability:</strong></p><ul><li>As the adversarial robustness of the teacher model decreases, the student model's reliance shifts from the teacher's guidance to more self-derived insights. This evolution in the learning strategy helps maintain effectiveness even as external conditions become more challenging.</li></ul></li><li><p><strong>Reliable Guidance Construction:</strong></p><ul><li>The strategy to segment the adversarial samples and analyze them to determine the reliability of the teacher’s predictions on each segment is a methodological approach that could be mirrored in other machine learning systems dealing with unreliable data sources or changing environments.</li></ul></li><li><p><strong>Visual and Quantitative Analysis:</strong></p><ul><li>Using visual tools like decision region illustrations and tracking changes in data reliability over time provides a clear and quantifiable way to adjust strategies, similar to how changes in game strategies might be analyzed in systems like TD-Gammon.</li></ul></li></ol><p>The concept of knowledge distillation, particularly in adversarial contexts, ties back to the fundamental issues of trust, reliability, and adaptation in machine learning. It underscores the importance of developing systems that not only learn from external inputs but also critically evaluate and adapt these learnings to enhance their robustness and performance over time.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r83:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-32" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb21ac4-d07e-4b1c-8d86-8d241c751ed0" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>5.3ABLATIONSTUDIES
To give a comprehensive understanding of our proposed IAD method, we have conducted a series
of experiments (in Appendix A), including the ablation study on using different γ related to student
introspection, differentτrelated to adversarial distillation and the loss terms of IAD-II as well as the
comparison of the computational cost. In the following, we only study the effect ofβand warming-up
periods for our student introspection. More ablation study can be found in the Appendix.
Experiment Setup.To understand the effects of differentβand different warming-up periods on
CIFAR-10 dataset, we conduct the ablation study in this part. Specif i cally, we choose the ResNet-18
as the backbone model, and keep the experimental settings the same as Section 5.1. In the i rst
experiments, we set no warming-up period and study the effect of using differentβ. Then, in the
second experiments, we set β = 0.1 and investigate different warming-up periods.
Results.We report part of the results on IAD-I method in Figure 4. The complete results with other
evaluation metrics as well as that on IAD-II method can be found in Appendix A.1. In Figure 4, we
i rst visualize the values of theαusing differentβin the left panel, which shows the proportion of the
teacher guidance and student introspection in adversarial distillation. The bigger the beta corresponds
to a larger proportion of the student introspection. In the middle panel, we plot the natural and
PGD-20 accuracy of the student models distilled by differentβ. We note that the PGD-20 accuracy is
improved when the student model trusts itself more with the largerβvalue. However, the natural
accuracy is decreasing along with the increasing of theβvalue. Similarly, we adjust the length of
warming-up periods and check the natural and PGD-20 accuracy in the right panel of Figure 4. We
i nd that setting the student model partially trust itself at the beginning of the training process leads
to inadequate robustness improvements. An appropriate warming-up period at the early stage can
improve the student model performance on the adversarial examples.
6CONCLUSION
In this paper, we study distillation from adversarially pre-trained models. We take a closer look at
adversarial distillation and discover that the guidance of teacher model is progressively unreliable by
considering the robustness. Hence, we explore the construction of reliable guidance in adversarial
distillation and propose a method for distillation from unreliable teacher models, i.e., Introspective
Adversarial Distillation. Our methods encourages the student model partially instead of fully trust the
guidance of the teacher model and gradually trust its self-introspection more to improve robustness.</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" fill-rule="evenodd" d="M13.293 4.293a4.536 4.536 0 1 1 6.414 6.414l-1 1-7.094 7.094A5 5 0 0 1 8.9 20.197l-4.736.79a1 1 0 0 1-1.15-1.151l.789-4.736a5 5 0 0 1 1.396-2.713zM13 7.414l-6.386 6.387a3 3 0 0 0-.838 1.628l-.56 3.355 3.355-.56a3 3 0 0 0 1.628-.837L16.586 11zm5 2.172L14.414 6l.293-.293a2.536 2.536 0 0 1 3.586 3.586z" clip-rule="evenodd"></path></svg></button></span></div></div></div></div></div></div></div></div></div></div><div class="w-full 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10.0943 25.9948 10.1554 25.7963 10.2712L16.0726 15.8858V11.9982C16.0715 11.9783 16.0753 11.9585 16.0837 11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="03df92af-445d-4586-99fa-ac9aa60f727f" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The ablation studies for the Introspective Adversarial Distillation (IAD) method, as discussed in the text, delve into experimental evaluations to better understand and optimize the variables influencing the distillation process. Specifically, these studies explore how the parameters β (beta) and the length of warming-up periods affect the student model's ability to incorporate and benefit from teacher guidance and self-introspection. Here's a breakdown of the methodology and findings:</p><h3>Experiment Setup</h3><ul><li><strong>Model and Dataset:</strong> The experiments are conducted using the CIFAR-10 dataset with ResNet-18 as the backbone model. This setup remains consistent with earlier sections to ensure comparability.</li><li><strong>Variable Manipulations:</strong><ul><li><strong>β (beta):</strong> This parameter regulates the balance between relying on the teacher’s guidance and the student’s own introspection during adversarial distillation. Initial experiments vary β to see its impact without any warming-up period.</li><li><strong>Warming-Up Periods:</strong> Subsequent experiments fix β at 0.1 and vary the length of warming-up periods to study their effect on the learning outcomes.</li></ul></li></ul><h3>Results and Observations</h3><ul><li><strong>Impact of β (beta):</strong><ul><li>The experiments demonstrate that increasing β enhances the student model's adversarial accuracy (e.g., PGD-20 accuracy) as it relies more on self-introspection rather than the teacher's input.</li><li>Conversely, higher β values lead to a decrease in natural accuracy, indicating a trade-off between robustness to adversarial attacks and performance on unaltered data.</li></ul></li><li><strong>Impact of Warming-Up Periods:</strong><ul><li>Adjusting warming-up periods affects the model’s early-stage learning dynamics. A proper warming-up period allows the student model to initially depend more on the teacher, gradually increasing reliance on its introspection.</li><li>The results suggest that too short a warming-up period may not provide sufficient foundation for the student model, potentially hampering robustness improvements.</li></ul></li></ul><h3>Conclusion</h3><p>The ablation studies elucidate the delicate balance required in adversarial distillation, particularly when navigating the reliability of teacher models. By adjusting parameters like β and the warming-up period, the IAD method seeks to optimize the blend of guidance and independent learning to improve the robustness of student models against adversarial attacks.</p><h3>Connections and Implications</h3><p>These studies connect well with the broader theme of learning in dynamic and challenging environments, such as those discussed in FLORA systems and TD-Gammon. Similar to how these systems adapt based on context or game developments, IAD adjusts based on the adversarial context:</p><ul><li><strong>Adaptation and Incremental Learning:</strong> Like FLORA's handling of concept drift, IAD adapts to the evolving adversarial landscape, modifying how much it trusts predefined guidance (teacher models).</li><li><strong>Balancing Efficiency and Effectiveness:</strong> The exploration of optimal warming-up periods and β values mirrors the strategic adjustments seen in TD-Gammon and other learning systems, aiming to find the best balance between rapid adaptation and long-term strategic gains.</li></ul><p>Overall, the methodology and findings from these ablation studies contribute to refining approaches in machine learning where trust in traditional models (teachers) is questioned, and greater autonomy (student introspection) is encouraged for enhanced performance and robustness.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden 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padding-left: 0px; width: 0px;">4</span><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-sm text-token-text-quaternary"><path fill="currentColor" fill-rule="evenodd" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414" clip-rule="evenodd"></path></svg></div></button></span></div></div></div><div class="pr-2 lg:pr-0"></div></div></div></div></div></div><div class="w-full text-token-text-primary" dir="auto" data-testid="conversation-turn-34" data-scroll-anchor="false"><div class="py-2 juice:py-[18px] px-3 text-base md:px-4 m-auto md:px-5 lg:px-1 xl:px-5"><div class="mx-auto flex flex-1 gap-3 text-base juice:gap-4 juice:md:gap-5 juice:lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="user" data-message-id="bbb2177b-87b5-45cf-afca-fcd95ec010cb" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden items-end rtl:items-start"><div class="relative max-w-[70%] rounded-3xl bg-[#f4f4f4] px-5 py-2.5 dark:bg-token-main-surface-secondary"><div>Could I get some metaphors and analogies to help explain the more difficult concepts?</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md"><path fill="currentColor" 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juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Certainly! Here are a few metaphors and analogies to help elucidate some complex concepts discussed in our conversations about machine learning, particularly focusing on adversarial distillation, concept drift, and learning mechanisms:</p><h3>1. <strong>Knowledge Distillation & Cooking</strong></h3><ul><li><strong>Metaphor:</strong> Imagine a master chef (teacher model) who knows exactly how to cook a sophisticated dish. A novice chef (student model) learns by watching and mimicking the master. However, if the ingredients (data) change unpredictably—say, swapping beef for tofu—the master’s instructions might not yield the same tasty result. This is like knowledge distillation, where the student learns from the teacher but must adjust the instructions based on slightly different ingredients (data scenarios).</li></ul><h3>2. <strong>Concept Drift & Shifting Sand Dunes</strong></h3><ul><li><strong>Analogy:</strong> Think of concept drift like walking on shifting sand dunes. As you walk (over time), the landscape (data environment) changes subtly beneath your feet. If you use the same map (model) that was effective in the morning, it might not be accurate in the afternoon because the dunes (concepts) have shifted. Just as you need to adjust your path, learning systems must update their understanding and strategies.</li></ul><h3>3. <strong>Adversarial Distillation & Training in Sports</strong></h3><ul><li><strong>Metaphor:</strong> Consider a sports coach training an athlete for high-altitude conditions by initially using an altitude training mask (teacher model providing robust guidance). As the athlete’s (student model’s) body adapts, the reliance on the mask decreases. The athlete learns to gauge their own capabilities and limitations better, reducing their dependence on the mask and trusting their own body’s responses (student introspection) more to achieve peak performance.</li></ul><h3>4. <strong>Unreliable Teachers & Navigating with an Old Map</strong></h3><ul><li><strong>Analogy:</strong> Using guidance from an unreliable teacher model is like navigating a city with an old map. While the map (teacher’s instructions) offers a general sense of direction, some roads (data scenarios) might have changed, and new paths (strategies) might need to be discovered on your own. This requires a mix of trusting the old map for familiar areas and exploring new areas independently.</li></ul><h3>5. <strong>FLORA Learning Mechanism & Gardening</strong></h3><ul><li><strong>Metaphor:</strong> Imagine a gardener tending to a diverse garden (data environment). As seasons change (context shifts), the plants’ needs (concept requirements) differ. The gardener must decide which plants need more water and which need less, similar to how FLORA adjusts its focus on different data examples, learning which concepts to nurture and which to let fade.</li></ul><h3>6. <strong>Student Introspection & Learning to Ride a Bike</strong></h3><ul><li><strong>Analogy:</strong> Think of a child learning to ride a bike with training wheels (teacher model). Initially, the training wheels provide necessary support. However, as the child gains balance and confidence (student introspection), they rely less on the training wheels and more on their own ability to navigate and balance, eventually riding without them.</li></ul><p>These metaphors and analogies can help in explaining complex machine learning concepts by relating them to more familiar everyday experiences, making the technical details more accessible and understandable.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 4.91a.5.5 0 0 0-.838-.369L6.676 7.737A1 1 0 0 1 6 8H4a1 1 0 0 0-1 1v6a1 1 0 0 0 1 1h2a1 1 0 0 1 .676.263l3.486 3.196A.5.5 0 0 0 11 19.09zM8.81 3.067C10.415 1.597 13 2.735 13 4.91v14.18c0 2.175-2.586 3.313-4.19 1.843L5.612 18H4a3 3 0 0 1-3-3V9a3 3 0 0 1 3-3h1.611zm11.507 3.29a1 1 0 0 1 1.355.401A10.96 10.96 0 0 1 23 12c0 1.85-.458 3.597-1.268 5.13a1 1 0 1 1-1.768-.934A8.96 8.96 0 0 0 21 12a8.96 8.96 0 0 0-1.085-4.287 1 1 0 0 1 .402-1.356M15.799 7.9a1 1 0 0 1 1.4.2 6.48 6.48 0 0 1 1.3 3.9c0 1.313-.39 2.537-1.06 3.56a1 1 0 0 1-1.673-1.096A4.47 4.47 0 0 0 16.5 12a4.47 4.47 0 0 0-.9-2.7 1 1 0 0 1 .2-1.4" clip-rule="evenodd"></path></svg></span></button></span><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z" clip-rule="evenodd"></path></svg></span></button></span><div class="flex"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11.873 21.496a1 1 0 0 1-.992.496l-.454-.056A4 4 0 0 1 7.1 16.79L7.65 15h-.718c-2.637 0-4.553-2.508-3.859-5.052l1.364-5A4 4 0 0 1 8.296 2h9.709a3 3 0 0 1 3 3v7a3 3 0 0 1-3 3h-2c-.26 0-.5.14-.628.364zM14.005 4h-5.71a2 2 0 0 0-1.929 1.474l-1.363 5A2 2 0 0 0 6.933 13h2.072a1 1 0 0 1 .955 1.294l-.949 3.084a2 2 0 0 0 1.462 2.537l3.167-5.543a2.72 2.72 0 0 1 1.364-1.182V5a1 1 0 0 0-1-1m3 9V5c0-.35-.06-.687-.171-1h1.17a1 1 0 0 1 1 1v7a1 1 0 0 1-1 1z" clip-rule="evenodd"></path></svg></span></button></span></div><span class="" data-state="closed"><button type="button" id="radix-:r8h:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="cursor-pointer rounded-md px-1 text-token-text-secondary h-[30px] hover:bg-token-main-surface-secondary"><div class="flex items-center pb-0.5 juice:pb-0"><div class="[&_svg]:h-full [&_svg]:w-full icon-md h-4 w-4"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24"><path fill="currentColor" d="M12.001 1.5a1 1 0 0 1 .993.887c.313 2.77 1.153 4.775 2.5 6.146 1.34 1.366 3.3 2.223 6.095 2.47a1 1 0 0 1-.003 1.993c-2.747.238-4.75 1.094-6.123 2.467-1.373 1.374-2.229 3.376-2.467 6.123a1 1 0 0 1-1.992.003c-.248-2.795-1.105-4.754-2.47-6.095-1.372-1.347-3.376-2.187-6.147-2.5a1 1 0 0 1-.002-1.987c2.818-.325 4.779-1.165 6.118-2.504 1.339-1.34 2.179-3.3 2.504-6.118A1 1 0 0 1 12 1.5ZM6.725 11.998c1.234.503 2.309 1.184 3.21 2.069.877.861 1.56 1.888 2.063 3.076.5-1.187 1.18-2.223 2.051-3.094.871-.87 1.907-1.55 3.094-2.05-1.188-.503-2.215-1.187-3.076-2.064-.885-.901-1.566-1.976-2.069-3.21-.505 1.235-1.19 2.3-2.081 3.192-.891.89-1.957 1.576-3.192 2.082Z"></path></svg></div><span class="line-clamp-1 text-sm" style="opacity: 0; 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Counterfoil Choices in the Kalabari Life Cycle
by Nimi Wariboko
INTRODUCTION
Kalabari ethnic identity is under enormous pressure as a result of modernization and Western influences. One Kalabari response to their exposure to foreign values, styles, cultural artifacts and ways of life has been to select, incorporate, and transform borrowed values, styles, and artifacts to create a new combination or ensemble uniquely identified as Kalabari. This process of adaptation has been described as cultural authentication (Erekosima and Eicher 1981,1995; Eicher 1997). In their studies, Erekosima and Eicher have focused only on the use of a limited number of material artifacts (such as textiles) to create and maintain ethnic identity. Kalabari have created clothing that separates them from their neighbors, “for items assembled from their history and the range of their trading contacts resulted in distinctive appearance” (Eicher 1997:231).
Why the preference for distinctive appearance? Why are the Kalabari always tinkering with foreign artifacts in order to make themselves distinct from their Southern Nigerian neighbors? Why the deep preference for independence? The best answer Eicher and colleagues have found is: “Kalabari dress represented their independence of thought and action and their view of a tripartite cosmology of the water-people, community deities and ancestors” (Eicher1997:231; Erekosima 1989, Daly 1984). This explanation appears inadequate. By limiting their analyses to the easily observable somewhat static connection between dress and world view, they ignore the more intellectual, dynamic, and complex process involved in maintaining and passing to the next generation the core of Kalabari identity. Maintaining an ethnic identity is not a one-time affair, especially for an African traditional society that has to grapple with influences both from the West and from other nationalities within Nigeria. Dress and other aspects of the culture are often the visible representations of an invisible world view. One is, however, very far from the whole truth unless one explains how this link has been maintained from pre-colonial times until today in spite of all influences to the contrary.
This paper discusses the salient management tool or idea that Kalabari have used and are still using to ensure that their ethnic identity is maintained amidst the flux of changes from within and outside. This paper brings to the fore the philosophical principles which put into proper perspective the Kalabari struggle to maintain an identity and way of life, and to minimize European influences on their traditional and political beliefs (Dike 1956: 161). For lack of a better terminology, this identity management tool is termed counterfoil choice.
In most societies, there are two types of choices: ordinary and Hobson. In ordinary choice, the decision-maker chooses between A or B, which are alternatives to each other. Hobson’s choice is between what is offered and nothing. Kalabari have a third variety wherein the freedom to choose is not limited as in Hobson’s choice, but the result of the selection is similar to that of Hobson’s choice. This is termed counterfoil choice. A is not an alternative to B; B is only a counterfoil to A. When A is offered, Kalabari offers its negative B to show the person where the decision should not go. The decision-maker is primed to choose A, the real “ticket” and shun the counterfoil. For instance, a father wanting to teach his child a lesson about success might give him two bowls. One contains garri (cassava derived flour), the other is empty. The child is asked to choose. The empty bowl is there to show that laziness comes with severe hunger and that life offers two bowls (prosperity/power or failure/disgrace). The child is advised to know the right bowl to choose. It is a counterfoil choice because no father wishes his son or daughter to choose the empty bowl. Kalabari have found this an effective way of teaching their youngsters.
The use of this management tool in Kalabari society parallels age-grade and political status. Thus, this essay shall proceed by examining the significance and role of counterfoil choice within Kalabari culture from the perspective of its relevance through the political life cycle. For the limited purposes here, the life cycle is divided into five stages: awome (birth to age 15), asawo (16 to 40), opuasawo (40 and above), alapu (chiefs) and duein (ancestors). Ancestor is considered a stage in the life cycle because a person’s life is deemed incomplete if he or she does not become an ancestor after death. To be an ancestor a person must be in good standing before entering the next world.
This classification is not precise; the purpose is only to indicate phases. It is based mainly on the male life cycle. However, this paper will consider women in the category of iya (most lawful and expensive) wives when it is dealing with alapu because in traditional Kalabari society every chief must have one iya wife. Also, in terms of achievement women value iya marriage as much as men value chieftaincy titles. Third, the fact that this paper is focused mainly on age categories of men does not mean that counterfoil choice as relating to women is given short shrift. As a matter of fact, various examples of counterfoil choices are given which span the life cycle of women in the society. This paper limits its focus only to men’s age categories because it is easier to handle five categories than handle 10 in short essay of this nature. Fourth, age is not the sole determinant of each category as personal wealth and achievement of an under-30 years can move a person to the rank of chiefs.
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Cultural Identity,Kalabari,Modernization,Nigeria
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11.9405C16.0921 11.9225 16.1048 11.9068 16.1207 11.8949L24.1719 7.25025C25.4053 6.53903 26.8158 6.19376 28.2383 6.25482C29.6608 6.31589 31.0364 6.78077 32.2044 7.59508C33.3723 8.40939 34.2842 9.53945 34.8334 10.8531C35.3826 12.1667 35.5464 13.6095 35.3055 15.0128ZM14.2424 21.9419L10.8752 19.9981C10.8576 19.9893 10.8423 19.9763 10.8309 19.9602C10.8195 19.9441 10.8122 19.9254 10.8098 19.9058V10.6071C10.8107 9.18295 11.2173 7.78848 11.9819 6.58696C12.7466 5.38544 13.8377 4.42659 15.1275 3.82264C16.4173 3.21869 17.8524 2.99464 19.2649 3.1767C20.6775 3.35876 22.0089 3.93941 23.1034 4.85067C23.0427 4.88379 22.937 4.94215 22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="bd63841a-5067-4b11-9409-5d6e47ab3eee" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>The exploration of Kalabari ethnic identity and its adaptation to external influences through the strategic use of cultural artifacts, particularly in the realm of dress, offers a rich parallel to various concepts in artificial intelligence, particularly in adaptive learning systems and the handling of concept drift. Here’s how the cultural dynamics of the Kalabari can be analogized to elements in machine learning and AI:</p><h3>1. <strong>Counterfoil Choice and Adversarial Learning</strong></h3><ul><li><strong>Analogy:</strong> In the Kalabari concept of counterfoil choice, a decision-maker is presented with options where one is clearly unfavorable, guiding the decision toward a preferred outcome. This is somewhat akin to adversarial learning in AI, where a model is trained not just on straightforward examples but also exposed to challenging or deceptive inputs (akin to the empty bowl). The purpose is to reinforce the learning of correct patterns and robust decision-making under misleading circumstances.</li></ul><h3>2. <strong>Cultural Authentication and Knowledge Distillation</strong></h3><ul><li><strong>Analogy:</strong> Just as the Kalabari people adapt foreign influences into a unique cultural expression that maintains their ethnic identity, knowledge distillation in AI involves transferring knowledge from a larger, often complex model (the foreign influence) to a smaller, more efficient model (the unique expression). This process ensures that the distilled model retains the core functional essence of the original but in a form that suits new or different applications.</li></ul><h3>3. <strong>Modernization and Concept Drift</strong></h3><ul><li><strong>Analogy:</strong> The pressure of modernization on the Kalabari is similar to concept drift in machine learning. Just as the Kalabari must continuously evolve their cultural practices to remain relevant amidst changing external influences, adaptive learning systems must update their knowledge base to maintain accuracy as the data they are trained on evolves over time.</li></ul><h3>4. <strong>Cultural Identity and Robust Machine Learning Models</strong></h3><ul><li><strong>Analogy:</strong> Kalabari’s use of clothing and other cultural artifacts to assert their identity amid globalization reflects the use of robust training in AI to ensure that models maintain their performance and do not succumb to errors when faced with data or situations that deviate from their training environment. This is crucial in creating AI systems that are dependable and perform consistently in varied real-world applications.</li></ul><h3>5. <strong>Preserving Core Values and Ensemble Methods in AI</strong></h3><ul><li><strong>Analogy:</strong> The Kalabari effort to preserve core cultural values amidst external changes can be likened to ensemble methods in machine learning, where multiple models or algorithms are combined to produce a better, more stable output. Just as the Kalabari integrate various elements to form a resilient cultural identity, ensemble methods integrate diverse predictions to withstand perturbations and improve decision accuracy.</li></ul><p>These analogies help illuminate complex AI concepts by comparing them to cultural processes that are perhaps more intuitive or visually imaginable, providing a bridge between computational theories and human social practices.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" 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fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="f1430ad7-8446-412f-964f-92cb6378f1e0" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Throughout our conversation, we explored a variety of complex topics related to machine learning, artificial intelligence, and cultural studies, examining how these concepts are implemented in different contexts and how they relate to each other. Here's a summary of the main points discussed along with their interconnections:</p><h3>1. <strong>TD-Gammon and Reinforcement Learning</strong></h3><ul><li>We started by discussing TD-Gammon, a neural network that uses reinforcement learning to play backgammon. This system is notable for its use of Temporal Difference (TD) learning, which allows it to learn optimal strategies through self-play without external guidance.</li></ul><h3>2. <strong>Concept Drift in Machine Learning</strong></h3><ul><li>We delved into the concept of drift in machine learning, discussing how dynamic environments can influence the effectiveness of predictive models. This led to an exploration of the FLORA systems, which adapt to new data by updating hypotheses about concepts based on new information.</li></ul><h3>3. <strong>Knowledge Distillation</strong></h3><ul><li>The discussion transitioned to knowledge distillation, particularly focusing on how it can be used for adversarial robustness. We talked about the process where a student model learns from a teacher model to improve its accuracy and robustness, reflecting on the need for models to adapt when the teacher’s input may not be entirely reliable.</li></ul><h3>4. <strong>Adversarial Learning and Distillation</strong></h3><ul><li>We explored adversarial learning in greater depth, examining the nuances of teaching a student model to handle adversarial inputs that could potentially deceive or mislead the model. This was connected to the broader theme of robustness in AI systems, akin to cultural adaptation strategies.</li></ul><h3>5. <strong>Cultural Authentication and Identity</strong></h3><ul><li>The conversation shifted to a cultural study of the Kalabari people, focusing on how they maintain their ethnic identity through the strategic use of clothing and other artifacts, a process known as cultural authentication. This was paralleled with the concept of knowledge distillation in AI, where essential features are preserved while adapting to new circumstances.</li></ul><h3><strong>Interconnections:</strong></h3><ul><li><p><strong>Adaptation Across Systems:</strong> Whether discussing TD-Gammon’s strategy evolution, FLORA’s handling of concept drift, or the Kalabari's cultural adaptation, a common theme is the need for systems—be they computational or cultural—to adapt in response to changing environments.</p></li><li><p><strong>Reliability and Robustness:</strong> Just as the Kalabari selectively integrate external influences to maintain a coherent cultural identity, adversarial distillation involves a selective trust approach where a student model learns to discern and integrate reliable elements from a teacher model to enhance its robustness.</p></li><li><p><strong>Learning and Teaching Dynamics:</strong> In both cultural and computational contexts, the dynamics of learning from teachers (whether they be cultural artifacts in Kalabari society or teacher models in AI) involve assessing, integrating, and sometimes challenging the information received to improve the learner's ability to navigate complex environments.</p></li><li><p><strong>Preservation Amid Change:</strong> The discussion about the Kalabari's preservation of identity despite modern influences mirrors the challenges in AI regarding maintaining model integrity in the face of data shifts and adversarial attacks.</p></li></ul><p>Overall, this conversation highlighted how adaptive learning mechanisms in AI could draw parallels to human cultural adaptations, providing a rich framework for understanding both fields more deeply and integratively.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 z-10 -mt-1 bg-token-main-surface-primary md:absolute md:border md:border-token-border-light md:hidden"><div class="flex items-center"><span 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22.8668 4.98473L14.9024 9.58517C14.7025 9.69878 14.5366 9.86356 14.4215 10.0626C14.3065 10.2616 14.2466 10.4877 14.2479 10.7175L14.2424 21.9419ZM16.071 17.9991L20.4018 15.4978L24.7325 17.9975V22.9985L20.4018 25.4983L16.071 22.9985V17.9991Z" fill="currentColor"></path></svg></div></div></div></div></div><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn"><div class="flex-col gap-1 md:gap-3"><div class="flex flex-grow flex-col max-w-full"><div data-message-author-role="assistant" data-message-id="8fe4f04a-0104-4c49-8657-ea902f7f4263" dir="auto" class="min-h-[20px] text-message flex flex-col items-start whitespace-pre-wrap break-words [.text-message+&]:mt-5 juice:w-full juice:items-end overflow-x-auto gap-2"><div class="flex w-full flex-col gap-1 juice:empty:hidden juice:first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert dark"><p>Absolutely! The concept of counterfoil choices in the Kalabari culture, where clearly wrong or unfavorable choices are presented alongside favorable ones, indeed parallels the use of adversarial examples in machine learning. Here’s a deeper look into how this analogy enriches our understanding of both concepts:</p><h3>Counterfoil Choices in Cultural Context</h3><p>In the Kalabari tradition, counterfoil choices serve as a pedagogical tool to guide individuals towards making decisions that align with cultural values and wisdom. The less desirable options are not real choices but serve to illuminate the consequences of wrong decisions. For example, a father may present his child with two bowls—one filled with food and the other empty—to teach the value of hard work and the repercussions of laziness.</p><h3>Adversarial Examples in Machine Learning</h3><p>In machine learning, particularly in training robust AI systems, adversarial examples play a similar role. These are inputs to a model that have been intentionally designed to cause the model to make a mistake; they’re like the empty bowl in the Kalabari example. They’re used during training to improve the model’s ability to perform well even when faced with tricky or deceptive inputs that it might encounter in the real world.</p><h3>Interconnections and Insights</h3><ul><li><p><strong>Teaching Through Contrasts:</strong> Just as counterfoil choices highlight the benefits of one option over another, adversarial examples teach AI models to distinguish between typical and atypical patterns, reinforcing their ability to discern and react appropriately under various circumstances.</p></li><li><p><strong>Enhancing Robustness:</strong> In both contexts, the presence of a clearly inferior choice or a misleading example helps to fortify the decision-making process—whether it's a human learning cultural norms or an AI system ensuring data integrity against potential threats.</p></li><li><p><strong>Preparation for Real-world Challenges:</strong> Counterfoil choices prepare individuals to make wise decisions in more complex real-life situations. Similarly, adversarial examples prepare AI systems to handle and mitigate potential threats and anomalies that could occur in operational environments.</p></li><li><p><strong>Dynamic Learning and Adaptation:</strong> Both methods require a dynamic and adaptive learning process. Kalabari individuals must understand and internalize why some choices are inferior, while AI systems must update and adjust their parameters to effectively handle adversarial inputs.</p></li></ul><p>This analogy not only helps in understanding the importance of adversarial examples in developing robust AI systems but also underscores a universal principle of learning and adaptation that transcends domains—from cultural practices to cutting-edge technology.</p></div></div></div></div><div class="mt-1 flex gap-3 empty:hidden juice:-ml-3"><div class="items-center justify-start rounded-xl p-1 flex"><div class="flex items-center"><span class="" data-state="closed"><button class="rounded-lg text-token-text-secondary hover:bg-token-main-surface-secondary"><span class="flex h-[30px] w-[30px] items-center justify-center"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewBox="0 0 24 24" class="icon-md-heavy"><path fill="currentColor" fill-rule="evenodd" d="M11 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[hidden] { display: none; }
[multiple], [type="date"], [type="datetime-local"], [type="email"], [type="month"], [type="number"], [type="password"], [type="search"], [type="tel"], [type="text"], [type="time"], [type="url"], [type="week"], select, textarea { --tw-shadow: 0 0 transparent; appearance: none; background-color: rgb(255, 255, 255); border-color: rgb(155, 155, 155); border-radius: 0px; border-width: 1px; font-size: 1rem; line-height: 1.5rem; padding: 0.5rem 0.75rem; }
[multiple]:focus, [type="date"]:focus, [type="datetime-local"]:focus, [type="email"]:focus, [type="month"]:focus, [type="number"]:focus, [type="password"]:focus, [type="search"]:focus, [type="tel"]:focus, [type="text"]:focus, [type="time"]:focus, [type="url"]:focus, [type="week"]:focus, select:focus, textarea:focus { --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: #2563eb; --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(1px + var(--tw-ring-offset-width)) var(--tw-ring-color); border-color: rgb(37, 99, 235); box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow); outline: transparent solid 2px; outline-offset: 2px; }
[dir="ltr"] [multiple]:focus, [dir="ltr"] [type="date"]:focus, [dir="ltr"] [type="datetime-local"]:focus, [dir="ltr"] [type="email"]:focus, [dir="ltr"] [type="month"]:focus, [dir="ltr"] [type="number"]:focus, [dir="ltr"] [type="password"]:focus, [dir="ltr"] [type="search"]:focus, [dir="ltr"] [type="tel"]:focus, [dir="ltr"] [type="text"]:focus, [dir="ltr"] [type="time"]:focus, [dir="ltr"] [type="url"]:focus, [dir="ltr"] [type="week"]:focus, [dir="ltr"] select:focus, [dir="ltr"] textarea:focus { --tw-ring-inset: var(--tw-empty,/*!*/ /*!*/); }
[dir="rtl"] [multiple]:focus, [dir="rtl"] [type="date"]:focus, [dir="rtl"] [type="datetime-local"]:focus, [dir="rtl"] [type="email"]:focus, [dir="rtl"] [type="month"]:focus, [dir="rtl"] [type="number"]:focus, [dir="rtl"] [type="password"]:focus, [dir="rtl"] [type="search"]:focus, [dir="rtl"] [type="tel"]:focus, [dir="rtl"] [type="text"]:focus, [dir="rtl"] [type="time"]:focus, [dir="rtl"] [type="url"]:focus, [dir="rtl"] [type="week"]:focus, [dir="rtl"] select:focus, [dir="rtl"] textarea:focus { --tw-ring-inset: var(--tw-empty, ); }
input::placeholder, textarea::placeholder { color: rgb(155, 155, 155); opacity: 1; }
::-webkit-datetime-edit-fields-wrapper { padding: 0px; }
::-webkit-date-and-time-value { min-height: 1.5em; }
::-webkit-datetime-edit, ::-webkit-datetime-edit-day-field, ::-webkit-datetime-edit-hour-field, ::-webkit-datetime-edit-meridiem-field, ::-webkit-datetime-edit-millisecond-field, ::-webkit-datetime-edit-minute-field, ::-webkit-datetime-edit-month-field, ::-webkit-datetime-edit-second-field, ::-webkit-datetime-edit-year-field { padding-bottom: 0px; padding-top: 0px; }
select { background-image: url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' viewBox='0 0 20 20'%3E%3Cpath stroke='%239B9B9B' stroke-linecap='round' stroke-linejoin='round' stroke-width='1.5' d='m6 8 4 4 4-4'/%3E%3C/svg%3E"); background-repeat: no-repeat; background-size: 1.5em 1.5em; -webkit-print-color-adjust: exact; }
[dir="ltr"] select { background-position: right 0.5rem center; padding-right: 2.5rem; }
[dir="rtl"] select { background-position: left 0.5rem center; padding-left: 2.5rem; }
[multiple] { background-image: none; background-position: 0px 0px; background-repeat: repeat; background-size: initial; -webkit-print-color-adjust: inherit; }
[dir="ltr"] [multiple] { padding-right: 0.75rem; }
[dir="rtl"] [multiple] { padding-left: 0.75rem; }
[type="checkbox"], [type="radio"] { --tw-shadow: 0 0 transparent; appearance: none; background-color: rgb(255, 255, 255); background-origin: border-box; border-color: rgb(155, 155, 155); border-width: 1px; color: rgb(37, 99, 235); display: inline-block; flex-shrink: 0; height: 1rem; padding: 0px; -webkit-print-color-adjust: exact; user-select: none; vertical-align: middle; width: 1rem; }
[type="checkbox"] { border-radius: 0px; }
[type="radio"] { border-radius: 100%; }
[type="checkbox"]:focus, [type="radio"]:focus { --tw-ring-offset-width: 2px; --tw-ring-offset-color: #fff; --tw-ring-color: #2563eb; --tw-ring-offset-shadow: var(--tw-ring-inset) 0 0 0 var(--tw-ring-offset-width) var(--tw-ring-offset-color); --tw-ring-shadow: var(--tw-ring-inset) 0 0 0 calc(2px + var(--tw-ring-offset-width)) var(--tw-ring-color); box-shadow: var(--tw-ring-offset-shadow),var(--tw-ring-shadow),var(--tw-shadow); outline: transparent solid 2px; outline-offset: 2px; }
[dir="ltr"] [type="checkbox"]:focus, [dir="ltr"] [type="radio"]:focus { --tw-ring-inset: var(--tw-empty,/*!*/ /*!*/); }
[dir="rtl"] [type="checkbox"]:focus, [dir="rtl"] [type="radio"]:focus { --tw-ring-inset: var(--tw-empty, ); }
[type="checkbox"]:checked, [type="radio"]:checked { background-color: currentcolor; background-position: 50% center; background-repeat: no-repeat; background-size: 100% 100%; border-color: transparent; }
[type="checkbox"]:checked { background-image: url("data:image/svg+xml;charset=utf-8,%3Csvg viewBox='0 0 16 16' fill='%23fff' xmlns='http://www.w3.org/2000/svg'%3E%3Cpath d='M12.207 4.793a1 1 0 0 1 0 1.414l-5 5a1 1 0 0 1-1.414 0l-2-2a1 1 0 0 1 1.414-1.414L6.5 9.086l4.293-4.293a1 1 0 0 1 1.414 0z'/%3E%3C/svg%3E"); }
[type="radio"]:checked { background-image: url("data:image/svg+xml;charset=utf-8,%3Csvg viewBox='0 0 16 16' fill='%23fff' xmlns='http://www.w3.org/2000/svg'%3E%3Ccircle cx='8' cy='8' r='3'/%3E%3C/svg%3E"); }
[type="checkbox"]:checked:focus, [type="checkbox"]:checked:hover, [type="radio"]:checked:focus, [type="radio"]:checked:hover { background-color: currentcolor; border-color: transparent; }
[type="checkbox"]:indeterminate { background-color: currentcolor; background-image: url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' viewBox='0 0 16 16'%3E%3Cpath stroke='%23fff' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M4 8h8'/%3E%3C/svg%3E"); background-position: 50% center; background-repeat: no-repeat; background-size: 100% 100%; border-color: transparent; }
[type="checkbox"]:indeterminate:focus, [type="checkbox"]:indeterminate:hover { background-color: currentcolor; border-color: transparent; }
[type="file"] { background: initial; border-color: inherit; border-radius: 0px; border-width: 0px; font-size: inherit; line-height: inherit; padding: 0px; }
[type="file"]:focus { outline: -webkit-focus-ring-color auto 1px; }
h1 { font-size: 1.875rem; line-height: 2.25rem; }
h1, h2, h3 { font-weight: 600; }
h2, h3 { font-size: 1.5rem; line-height: 2rem; }
input[type="number"]::-webkit-inner-spin-button, input[type="number"]::-webkit-outer-spin-button { appearance: none; margin: 0px; }
*, ::after, ::before { --tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; --tw-rotate: 0; --tw-skew-x: 0; --tw-skew-y: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-pan-x: ; --tw-pan-y: ; --tw-pinch-zoom: ; --tw-scroll-snap-strictness: proximity; --tw-gradient-from-position: ; --tw-gradient-via-position: ; --tw-gradient-to-position: ; --tw-ordinal: ; --tw-slashed-zero: ; --tw-numeric-figure: ; --tw-numeric-spacing: ; --tw-numeric-fraction: ; --tw-ring-inset: ; --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-shadow: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-shadow-colored: 0 0 transparent; --tw-blur: ; --tw-brightness: ; --tw-contrast: ; --tw-grayscale: ; --tw-hue-rotate: ; --tw-invert: ; --tw-saturate: ; --tw-sepia: ; --tw-drop-shadow: ; --tw-backdrop-blur: ; --tw-backdrop-brightness: ; --tw-backdrop-contrast: ; --tw-backdrop-grayscale: ; --tw-backdrop-hue-rotate: ; --tw-backdrop-invert: ; --tw-backdrop-opacity: ; --tw-backdrop-saturate: ; --tw-backdrop-sepia: ; --tw-contain-size: ; --tw-contain-layout: ; --tw-contain-paint: ; --tw-contain-style: ; }
::backdrop { --tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; --tw-rotate: 0; --tw-skew-x: 0; --tw-skew-y: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-pan-x: ; --tw-pan-y: ; --tw-pinch-zoom: ; --tw-scroll-snap-strictness: proximity; --tw-gradient-from-position: ; --tw-gradient-via-position: ; --tw-gradient-to-position: ; --tw-ordinal: ; --tw-slashed-zero: ; --tw-numeric-figure: ; --tw-numeric-spacing: ; --tw-numeric-fraction: ; --tw-ring-inset: ; --tw-ring-offset-width: 0px; --tw-ring-offset-color: #fff; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-shadow: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-shadow-colored: 0 0 transparent; --tw-blur: ; --tw-brightness: ; --tw-contrast: ; --tw-grayscale: ; --tw-hue-rotate: ; --tw-invert: ; --tw-saturate: ; --tw-sepia: ; --tw-drop-shadow: ; --tw-backdrop-blur: ; --tw-backdrop-brightness: ; --tw-backdrop-contrast: ; --tw-backdrop-grayscale: ; --tw-backdrop-hue-rotate: ; --tw-backdrop-invert: ; --tw-backdrop-opacity: ; --tw-backdrop-saturate: ; --tw-backdrop-sepia: ; --tw-contain-size: ; --tw-contain-layout: ; --tw-contain-paint: ; --tw-contain-style: ; }
:root { --white: #fff; --black: #000; --gray-50: #f9f9f9; --gray-100: #ececec; --gray-200: #e3e3e3; --gray-300: #cdcdcd; --gray-400: #b4b4b4; --gray-500: #9b9b9b; --gray-600: #676767; --gray-700: #424242; --gray-750: #2f2f2f; --gray-800: #212121; --gray-900: #171717; --gray-950: #0d0d0d; --red-500: #ef4444; --red-700: #b91c1c; --brand-purple: #ab68ff; }
html { --text-primary: var(--gray-950); --text-secondary: var(--gray-500); --text-tertiary: var(--gray-400); --text-quaternary: var(--gray-300); --text-error: var(--red-700); --surface-error: var(--red-700); --border-light: rgba(0,0,0,.1); --border-medium: rgba(0,0,0,.15); --border-heavy: rgba(0,0,0,.2); --border-xheavy: rgba(0,0,0,.25); --main-surface-primary: var(--white); --main-surface-secondary: var(--gray-50); --main-surface-tertiary: var(--gray-100); --sidebar-surface-primary: var(--gray-50); --sidebar-surface-secondary: var(--gray-100); --sidebar-surface-tertiary: var(--gray-200); --link: #2964aa; --link-hover: #749ac8; --selection: #007aff; }
html.ZnJ1aXRqdWljZQ { --text-secondary: #7d7d7d; --text-error: #f93a37; --surface-error: 249 58 55; }
.dark { --text-primary: var(--gray-100); --text-secondary: var(--gray-300); --text-tertiary: var(--gray-400); --text-quaternary: var(--gray-500); --text-error: var(--red-500); --border-light: hsla(0,0%,100%,.1); --border-medium: hsla(0,0%,100%,.15); --border-heavy: hsla(0,0%,100%,.2); --border-xheavy: hsla(0,0%,100%,.25); --main-surface-primary: var(--gray-800); --main-surface-secondary: var(--gray-750); --main-surface-tertiary: var(--gray-700); --sidebar-surface-primary: var(--gray-900); --sidebar-surface-secondary: var(--gray-800); --sidebar-surface-tertiary: var(--gray-750); --link: #7ab7ff; --link-hover: #5e83b3; }
html.ZnJ1aXRqdWljZQ.dark { --text-secondary: var(--gray-400); --text-tertiary: var(--gray-500); --text-quaternary: var(--gray-600); --text-error: #f93a37; --surface-error: 249 58 55; }
.popover { --main-surface-primary: var(--white) !important; --main-surface-secondary: var(--gray-100) !important; --main-surface-tertiary: var(--gray-200) !important; --sidebar-surface-primary: var(--white) !important; }
.dark .popover, .dark.popover, .popover .dark { --main-surface-primary: var(--gray-750) !important; --main-surface-secondary: var(--gray-700) !important; --main-surface-tertiary: var(--gray-600) !important; --text-primary: var(--gray-50) !important; --text-secondary: var(--gray-200) !important; --text-tertiary: var(--gray-400) !important; --text-quaternary: var(--gray-500) !important; --sidebar-surface-primary: var(--gray-750) !important; }
textarea:focus { border-color: inherit; box-shadow: none; outline: none; }
.container { width: 100%; }
@media (min-width: 640px) {
.container { max-width: 640px; }
}
@media (min-width: 768px) {
.container { max-width: 768px; }
}
@media (min-width: 1024px) {
.container { max-width: 1024px; }
}
@media (min-width: 1280px) {
.container { max-width: 1280px; }
}
@media (min-width: 1536px) {
.container { max-width: 1536px; }
}
.prose { color: var(--tw-prose-body); max-width: 65ch; }
.prose :where([class~="lead"]):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-lead); font-size: 1.25em; line-height: 1.6; margin-bottom: 1.2em; margin-top: 1.2em; }
.prose :where(a):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-links); font-weight: 500; text-decoration: underline; }
.prose :where(strong):not(:where([class~="not-prose"] *)) { color: var(--tw-prose-bold); font-weight: 600; }
.prose :where(a strong):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(blockquote strong):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(thead th strong):not(:where([class~="not-prose"] *)) { color: inherit; }
.prose :where(ol):not(:where([class~="not-prose"] *)) { list-style-type: decimal; margin-bottom: 1.25em; margin-top: 1.25em; }
[dir="ltr"] .prose :where(ol):not(:where([class~="not-prose"] *)) { padding-left: 1.625em; }
[dir="rtl"] .prose :where(ol):not(:where([class~="not-prose"] *)) { padding-right: 1.625em; }
.prose :where(ol[type="A"]):not(:where([class~="not-prose"] *)) { list-style-type: upper-alpha; }
.prose :where(ol[type="a"]):not(:where([class~="not-prose"] *)) { list-style-type: lower-alpha; }
.prose :where():not(:where([class~="not-prose"] *)) { list-style-type: upper-alpha; }
.prose :where():not(:where([class~="not-prose"] *)) { list-style-type: lower-alpha; }
.prose :where(ol[type="I"]):not(:where([class~="not-prose"] *)) { list-style-type: upper-roman; }
.prose :where(ol[type="i"]):not(:where([class~="not-prose"] *)) { list-style-type: lower-roman; }
.prose :where():not(:where([class~="not-prose"] *)) { list-style-type: upper-roman; }
.prose :where():not(:where([class~="not-prose"] *)) { list-style-type: lower-roman; }
.prose :where(ol[type="1"]):not(:where([class~="not-prose"] *)) { list-style-type: decimal; }
.prose :where(ul):not(:where([class~="not-prose"] *)) { list-style-type: disc; margin-bottom: 1.25em; margin-top: 1.25em; }
[dir="ltr"] .prose :where(ul):not(:where([class~="not-prose"] *)) { padding-left: 1.625em; }
[dir="rtl"] .prose :where(ul):not(:where([class~="not-prose"] *)) { padding-right: 1.625em; }