Evidence of Learned Look-Ahead in a Chess-Playing Neural Network

TL;DR

This paper provides evidence that a neural chess engine, Leela Chess Zero, learns to internally represent future moves and look-ahead strategies, revealing complex planning capabilities beyond simple heuristics.

Contribution

It demonstrates that transformer-based neural networks can learn and utilize look-ahead in chess, with multiple lines of evidence showing internal representations of future moves.

Findings

Activations on future move squares are causally important.

Attention heads encode information about future moves.

A probe predicts 2-move-ahead optimal moves with 92% accuracy.

Abstract

Do neural networks learn to implement algorithms such as look-ahead or search "in the wild"? Or do they rely purely on collections of simple heuristics? We present evidence of learned look-ahead in the policy network of Leela Chess Zero, the currently strongest neural chess engine. We find that Leela internally represents future optimal moves and that these representations are crucial for its final output in certain board states. Concretely, we exploit the fact that Leela is a transformer that treats every chessboard square like a token in language models, and give three lines of evidence (1) activations on certain squares of future moves are unusually important causally; (2) we find attention heads that move important information "forward and backward in time," e.g., from squares of future moves to squares of earlier ones; and (3) we train a simple probe that can predict the optimal move 2 turns ahead with 92% accuracy (in board states where Leela finds a single best line). These findings are an existence proof of learned look-ahead in neural networks and might be a step towards a better understanding of their capabilities.