Acquisition of Chess Knowledge in AlphaZero

[daniel]

One of the first interesting outcomes of the first published games from Alpha Zero was that the program "rediscovered" the Berlin Defense, GM Kramnik's invention and weapon in his WC match against Kasparov.
This is interesting, because before this, established view on chess engines was, that they do require an opening database - the fruits of hundreds of years of human chess culture. Now, a program on a modern machine can invent openings, and do other creative work.

This article, in parts, is rather technical, detailed.
However, do not be scared! It also delivers valuable insights for the chess player.
Moreover, note, that no other than Kramnik himself coauthored this paper!

Enjoy the read!

Daniel

---

link: https://arxiv.org/pdf/2111.09259.pdf

Title: Acquisition of Chess Knowledge in AlphaZero

Authors: Thomas McGrath, Andrei Kapishnikov, Nenad Tomasev, Adam Pearce, Demis Hassabis, Been Kim, Ulrich Paquet, Vladimir Kramnik

Abstract:

"
What is learned by sophisticated neural network agents such as AlphaZero? This question is of both scientific and practical
interest. If the representations of strong neural networks bear no resemblance to human concepts, our ability to understand
faithful explanations of their decisions will be restricted, ultimately limiting what we can achieve with neural network interpretability.
In this work we provide evidence that human knowledge is acquired by the AlphaZero neural network as it trains on the game
of chess. By probing for a broad range of human chess concepts we show when and where these concepts are represented
in the AlphaZero network. We also provide a behavioural analysis focusing on opening play, including qualitative analysis
from chess Grandmaster Vladimir Kramnik. Finally, we carry out a preliminary investigation looking at the low-level details of
AlphaZero’s representations, and make the resulting behavioural and representational analyses available online.
"

[daniel]

Author: Marc Barthelemy, https://www.researchgate.net/profile/Marc-Barthelemy-4

Abstract
"
We introduce a metric to quantify the fragility of chess positions using the interaction graph of pieces. This fragility score 𝐹 captures the tension within a position and serves as a strong indicator of tipping points in a game. In well-known games, maximum fragility often aligns with decisive moments marked by brilliant moves. Analyzing a large dataset of games, we find that fragility typically peaks around move 15, with pawns (≈60%) and knights (≈20%) frequently involved in high-tension positions. Comparing the Stockfish evaluation with the fragility score, we observe that the maximum fragility ply often serves as a critical turning point, where the moves made afterward can determine the outcome of the game. Remarkably, average fragility curves show a universal pattern across a wide range of players, games, and openings, with a subtle deviation observed in games played by the engine Stockfish. Our analysis reveals a gradual buildup of fragility starting around eight moves before the peak, followed by a prolonged fragile state lasting up to 15 moves. This suggests a gradual intensification of positional tension leading to decisive moments in the game. These insights offer a valuable tool for both players and engines to assess critical moments in chess.
"

Preprint: https://www.researchgate.net/publicatio ... ing_points

appeared in PhysRevE (behind paywall)
https://journals.aps.org/pre/abstract/1 ... 111.014314