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Predicting Chess Puzzle Difficulty with Transformers

Szymon Miłosz, Paweł Kapusta

TL;DR

This work tackles the problem of predicting chess puzzle difficulty by modeling human cognitive processing rather than purely optimizing for gameplay outcome. It introduces GlickFormer, a transformer-based architecture that combines a ChessFormer spatial backbone with two temporal modeling variants to approximate Glicko-2 puzzle ratings. On a large Lichess puzzle corpus, GlickFormer outperforms the ChessFormer baseline across MAE, MAZ, and accuracy within rating deviations, with the Factorized Encoder variant achieving the best MAE of 217.71 and 67.66% accuracy within 3RD. The results demonstrate the value of explicit temporal modeling in cognitive tasks and indicate potential for personalized training and broader educational AI applications.

Abstract

This study addresses the challenge of quantifying chess puzzle difficulty - a complex task that combines elements of game theory and human cognition and underscores its critical role in effective chess training. We present GlickFormer, a novel transformer-based architecture that predicts chess puzzle difficulty by approximating the Glicko-2 rating system. Unlike conventional chess engines that optimize for game outcomes, GlickFormer models human perception of tactical patterns and problem-solving complexity. The proposed model utilizes a modified ChessFormer backbone for spatial feature extraction and incorporates temporal information via factorized transformer techniques. This approach enables the capture of both spatial chess piece arrangements and move sequences, effectively modeling spatio-temporal relationships relevant to difficulty assessment. Experimental evaluation was conducted on a dataset of over 4 million chess puzzles. Results demonstrate GlickFormer's superior performance compared to the state-of-the-art ChessFormer baseline across multiple metrics. The algorithm's performance has also been recognized through its competitive results in the IEEE BigData 2024 Cup: Predicting Chess Puzzle Difficulty competition, where it placed 11th. The insights gained from this study have implications for personalized chess training and broader applications in educational technology and cognitive modeling.

Predicting Chess Puzzle Difficulty with Transformers

TL;DR

This work tackles the problem of predicting chess puzzle difficulty by modeling human cognitive processing rather than purely optimizing for gameplay outcome. It introduces GlickFormer, a transformer-based architecture that combines a ChessFormer spatial backbone with two temporal modeling variants to approximate Glicko-2 puzzle ratings. On a large Lichess puzzle corpus, GlickFormer outperforms the ChessFormer baseline across MAE, MAZ, and accuracy within rating deviations, with the Factorized Encoder variant achieving the best MAE of 217.71 and 67.66% accuracy within 3RD. The results demonstrate the value of explicit temporal modeling in cognitive tasks and indicate potential for personalized training and broader educational AI applications.

Abstract

This study addresses the challenge of quantifying chess puzzle difficulty - a complex task that combines elements of game theory and human cognition and underscores its critical role in effective chess training. We present GlickFormer, a novel transformer-based architecture that predicts chess puzzle difficulty by approximating the Glicko-2 rating system. Unlike conventional chess engines that optimize for game outcomes, GlickFormer models human perception of tactical patterns and problem-solving complexity. The proposed model utilizes a modified ChessFormer backbone for spatial feature extraction and incorporates temporal information via factorized transformer techniques. This approach enables the capture of both spatial chess piece arrangements and move sequences, effectively modeling spatio-temporal relationships relevant to difficulty assessment. Experimental evaluation was conducted on a dataset of over 4 million chess puzzles. Results demonstrate GlickFormer's superior performance compared to the state-of-the-art ChessFormer baseline across multiple metrics. The algorithm's performance has also been recognized through its competitive results in the IEEE BigData 2024 Cup: Predicting Chess Puzzle Difficulty competition, where it placed 11th. The insights gained from this study have implications for personalized chess training and broader applications in educational technology and cognitive modeling.

Paper Structure

This paper contains 15 sections, 28 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Dataset
  4. Methodology
  5. Puzzle Encoding
  6. Model Architecture
  7. Spatial Feature Extraction
  8. Incorporating Temporal Information
  9. Training Objective
  10. Implementation Details
  11. Experiments
  12. Experimental Setup
  13. Baseline Model
  14. Results and Analysis
  15. Conclusion

Figures (4)

  • Figure 1: Example of a simple two-move chess puzzle; White played Bb4 attacking Black's rook which is a blunder (left). The goal of the puzzle is to find the Qd4+! move, a fork attacking both the White king and bishop (right). In the next move White is forced to move the king or block the check, leaving the bishop undefended. Black then captures the unprotected bishop with Qxb4, resolving the puzzle by gaining material through the capture.
  • Figure 2: Distributions of selected dataset statistics
  • Figure 3: We propose two different architectures that incorporate temporal information processing mechanisms on top of the baseline ChessFormer model. Additionally, we modify the positional embedding schemes to address the architectural modifications.
  • Figure 4: Mean Absolute Error of each model depending on number of moves required to solve the puzzle.