Conditional Generation of Creative Chess Puzzles with Diffusion Models

Recent work has fine-tuned language models on chess data and reported high benchmark scores as evidence that the resulting models can understand the rules of chess, play full chess games at a professional level, or generate human-readable explanations grounded in expert knowledge. We train KinGPT, a 25M-parameter character-level language model trained only on (position, best-move) pairs, who exceeds 3B-parameter ChessGPT on a 600-puzzle mate-in-N suite and 4B-parameter C1-4B over a 20-theme puzzle benchmark. We examine several claims made in existing literature regarding chess-trained language models and assert that their impressive benchmark performance is largely explained by pattern-matching. We also demonstrate how LLM-Modulo, a verifier-in-the-loop framework, raises RedPajama 3B's best move accuracy from 1.2% to 21.2% and move generation validity from 19.3% to 95.3% on mate-in-N chess puzzles, comparable to gains achieved from ChessGPT's fine-tuning on chess-specific web corpora at a fraction of the cost. Our results illustrate how pairing a general LLM with an external verifier offers a more flexible alternative to directly training on synthetic data for well-defined domains. We open source all training/evaluation code, datasets, puzzle samples, and KinGPT model checkpoints for reproducibility.

In this paper, we introduce Representation Prediction via Autoencoding using Iterative Refinement (RePAIR) - a novel self-supervised representation learning architecture that synthesizes Masked Autoencoders (MAE), Joint Embedding Predictive Architectures (JEPA), and Bidirectional Encoder Representations from Transformers (BERT). We demonstrate how it can be used to encode objects in sequential data like consecutive chess positions into compact yet meaningful representations. The basic principle of the architecture is to mask large portions of a sequence of latent states, similar to BERT and MAE. Then, we apply a lightweight Predictor to the latent representations that repairs gaps in the sequence in a lower-dimensional embedding space akin to JEPA. Our experiments in the domain of chess show that the Encoder refines the board representations such that meaningful chess concepts emerge clustered in the latent space. Furthermore, reconstructions of the masked board states show that the model is able to reason about the piece movements without relying on costly reinforcement learning methods. Lastly, we find that the resulting representation space allows for quick and intuitive dissections of chess games by observing the game path trajectories in this semantically rich space.

Evaluating large language models becomes increasingly challenging as their capabilities advance: benchmarks can saturate, public test sets risk contamination, and assessing harder tasks can require expensive grading or execution infrastructure. These challenges are amplified in automatic prompt optimization (APO), where evaluation is repeated throughout the search for better prompts. Studying APO therefore requires a benchmark that is cheap and deterministic to score, hard enough to leave room for improvement, and renewable as models evolve. We introduce a chess benchmark built from 1,118 Lichess puzzles to study APO for frozen LLMs: we optimize their prompts without updating their model weights. Chess combines inexpensive exact-match scoring, engine-based evaluation of alternative moves, and a renewable supply of problems with adjustable difficulty. Unlike evaluations that report only success on isolated test items, the benchmark also connects puzzle-solving gains to short game-play rollouts within the same domain. We use it to evaluate six APO algorithms on eight target models, measuring not only baseline strength but also how much each model responds to optimization and whether optimized prompts transfer across models and to game play. Chess is thus a well-suited benchmark for APO: it is (i) challenging, as even the strongest evaluated model, Gemini 3.5 Flash (used as the meta-model), solves only about 55% of puzzles; (ii) discriminative, revealing gains, unchanged performance, and regressions across methods and models; (iii) renewable, with fresh puzzles to reduce contamination risk and adjustable difficulty to maintain headroom as models improve; and (iv) affordable, as the complete study runs for around $800. We release the puzzles, optimization and evaluation code, and dataset-renewal scripts (https://github.com/imec-ailabs/Automatic-Prompt-Optimization-with-Chess).