ChessSR: Using Symbolic Regression to Make Chess Evaluation Functions More Interpretable

The ChessSR project combines modern chess engine technology and symbolic regression algorithms, aiming to replace black-box neural network evaluation functions with understandable mathematical formulas, while maintaining evaluation capabilities close to Stockfish and solving the interpretability dilemma of chess AI.

Modern chess engines have surpassed human champions, but most are opaque black boxes: Stockfish relies on complex manually tuned evaluation functions, and the decision-making processes of neural network engines like AlphaZero are difficult to understand. This lack of interpretability leads to problems such as learning difficulties (humans struggle to extract strategies), research obstacles (hard to diagnose and improve), and low educational value. The ChessSR project addresses this by proposing to use symbolic regression technology to discover concise formulas from data, balancing evaluation accuracy and interpretability.

Symbolic regression is a machine learning technique whose goal is to discover mathematical expressions describing relationships in data (searching for both structure and parameters) rather than just fitting parameters. In chess evaluation, the task is to find a formula that takes chess position features (piece positions, number of pieces, etc.) as input and outputs a score close to Stockfish's evaluation, given the position and Stockfish's value. The project uses the PySR library (based on evolutionary algorithms, which automatically explore the formula space) to implement symbolic regression.

ChessSR uses a hybrid architecture: the C++ core implements engine functions such as position representation and move generation; the evaluation function is a pluggable module that supports traditional manual evaluation (SimpleEval) and symbolic regression evaluation (SymbolicEval). Current progress: The symbolic regression formula has an average error of 280 centipawns (about 2.8 pawns' value), with the goal of reducing it to 100 centipawns.

Symbolic regression formulas are concise and interpretable (e.g., "0.5queen count +3.2central control -2.1*king exposure"), while neural networks have millions of weight parameters that are hard to understand. This interpretability is of great significance for teaching (intuitively learning the weights of factors), research (discovering new heuristics), and manual adjustment (directly modifying formula coefficients).

Technology stack division: C++ handles core logic (to ensure performance), Python handles symbolic regression training (taking advantage of PySR's convenience). The UI currently only supports Linux terminals (using Unicode to draw the chessboard), and developers are looking for cross-platform solutions.

Current limitations: Insufficient evaluation accuracy (280 centipawn error), failure to capture advanced strategic concepts such as pawn structure and spatial advantage. Future directions: Optimize symbolic regression training (feature engineering, larger datasets), explore the combination of symbolic regression and neural networks, and organize formulas for teaching and research.

ChessSR is an interesting attempt in the field of interpretable AI. It does not aim to be the strongest engine but to explore AI transparency. Symbolic regression provides a feasible path to achieve this goal. Whether it eventually reaches the level of top engines or not, it offers a new perspective for chess AI research and accumulates practical experience in interpretable AI.