Generalization or Memorization? Brittleness Testing for Chess-Trained Language Models

Language models often lack grounded reasoning capabilities in specialized domains where training data is scarce but bespoke systems excel. We introduce a general framework for distilling expert system reasoning into natural language chain-of-thought explanations, enabling compact models to acquire domain expertise and the ability to generate faithful, grounded explanations. Rather than distilling only final outputs, we capture the full reasoning process, transforming opaque expert computations into transparent, step-by-step explanations. We demonstrate this approach in chess, a canonical reasoning domain where language models continue to underperform. Our 4B parameter model, C1, advances from a near-zero baseline to 48.1% accuracy, outperforming all open-source models and most frontier proprietary systems. Notably, C1 surpasses its distillation teacher and generates solutions in two orders of magnitude fewer tokens than baselines. Unlike prior neural chess approaches that predict only best moves, C1 generates explainable solutions revealing strategic reasoning. Our pipeline combines supervised fine-tuning and reinforcement learning with theme-balanced data sampling for comprehensive tactical coverage. Master Distillation demonstrates how to inject expert-level knowledge into compact models for under-optimized domains, offering a recipe for unlocking RLVR where LLMs lack sufficient base capabilities.

Superhuman game engines in domains like chess have made expert-level evaluations easily accessible, yet they communicate what is true without the natural-language explanations that make such expertise educationally useful to experts and non-experts alike. Large language models could, in principle, bridge this gap, but they frequently hallucinate due to limited domain-specific knowledge, and standard reference-based or LLM-as-a-judge frameworks cannot reliably detect these errors. In this work, we present ACT-Eval, an evaluation framework that decomposes chess commentary into atomic claims and routes them to engine-supported tools and expert-annotated gold references to assess factual correctness, conceptual coverage, and move-quality judgment. We release a benchmark of 325 position--move pairs spanning pedagogical, tournament, and critical positions, including 125 positions with expert-verified gold atoms and a five-class error taxonomy. Evaluating leading proprietary and open-weight models, we find that factual hallucinations remain pervasive in chess commentary: GPT-5.4 without tools produces incorrect sub-claims 22.0% of the time, while smaller open-weight models exceed 40%. Although tool augmentation substantially improves factual correctness and move-quality assessment, coverage of expert strategic and tactical ideas remains limited across all models. Human calibration shows that ACT-Eval's factual judgments fall within the observed range of inter-human agreement, while its coverage scores correlate strongly with human assessments of strategic completeness.

World models require state tracking, which is the ability to maintain a correct latent state across action sequences. Existing benchmarks are often synthetic or language-based, limiting their value as tests of structured state updates in realistic domains. We introduce Chess-World-Model, a large-scale state-tracking benchmark built from 10 million real chess games, where models predict the exact board state reached after a sequence of legal moves. Alongside a held-out real-game split, we include an out-of-distribution split from uniformly random legal play, which tests whether models learn the transition rules rather than shortcuts from common human positions. Prior theoretical and empirical work has shown that Transformers struggle to state-track, while input-dependent linear RNNs require expressive state-transition matrices to do so. We therefore benchmark a causal Transformer, block-diagonal SLiCE, Mamba-3, and Gated DeltaNet with negative eigenvalues under a matched interface and training protocol. The recurrent models strongly outperform the Transformer at 3 and 8 million parameters. Real-game performance saturates above 18 million parameters, but the random-uniform split remains discriminative up to 40 million, exposing failures otherwise hidden by scale. Additionally, ablations show that less expressive state-transition mechanisms reduce performance on the out-of-distribution split for all three recurrent models. Together, these results establish Chess-World-Model as a practical large-scale benchmark for state tracking that exposes failures model scale would otherwise conceal.