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A z score (or standardized value) is measured in units of the standard deviation. It indicates how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z scores, and values of x that are smaller than the mean have negative z scores. If x equals the mean, then x has a zero z score. It is important to note that the mean of the z scores is zero, and the standard deviation is one.
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Updated: Aug 22, 2025

The Double-H Maze: A Robust Behavioral Test for Learning and Memory in Rodents
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Acquisition of chess knowledge in AlphaZero.

Thomas McGrath1, Andrei Kapishnikov2, Nenad Tomašev1

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Proceedings of the National Academy of Sciences of the United States of America
|November 14, 2022
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AlphaZero, a chess AI, learns human-like strategies by playing itself. Analysis reveals how its neural network represents these concepts, offering insights into artificial intelligence learning.

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artificial intelligencedeep learninginterpretabilitymachine learningreinforcement learning

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Area of Science:

  • Artificial Intelligence
  • Computational Neuroscience
  • Game Theory

Background:

  • AlphaZero, a neural network engine, learns chess independently.
  • It achieves superhuman performance without human game data.

Purpose of the Study:

  • To analyze the knowledge acquired by AlphaZero.
  • To understand how AlphaZero represents human-analogous chess concepts.
  • To investigate the internal workings of a self-learning AI.

Main Methods:

  • Utilized linear probes on AlphaZero's internal network states.
  • Quantified concept representation within the neural network.
  • Conducted a behavioral analysis of AlphaZero's opening game strategies.

Main Results:

  • Identified specific internal states where chess concepts are represented.
  • Demonstrated that AlphaZero learns concepts similar to human players.
  • Opening analysis, with expert commentary, revealed strategic depth.

Conclusions:

  • AlphaZero's self-play learning leads to the acquisition of human-analogous chess knowledge.
  • Internal network analysis provides a window into AI concept representation.
  • The findings contribute to understanding AI learning and strategic development.