Chess

Chess has long served as a model domain for studying search, expertise, decision-making, and artificial intelligence. The emergence of large language models (LLMs) has renewed the relevance of chess as a controlled environment for investigating strategic reasoning and comparing human and artificial decision-making. We present a systematic mapping study of recent research spanning human players, classical chess engines, neural and reinforcement-learning systems, LLMs, and hybrid approaches. The final map comprises 84 core study families, classified according to agent type, strategic-reasoning stages, and evaluation dimensions. The map reveals a literature strongly concentrated on situation assessment, evaluation, and action selection, while explicit planning, explanation, metacognition, and human--AI collaboration remain less explored. LLM research places particular emphasis on state representation and generalization, whereas grounded explanation appears more frequently in hybrid approaches combining language models with engines, expert knowledge, or other external structures. Two distinctions emerge that the map aggregates rather than resolves: hybrid systems differ in where and when heterogeneous capabilities combine, and evaluations that show improved human performance do not thereby establish human--AI synergy. We propose both as extensions of the mapping framework. We argue that chess provides a useful bridge between cognitive and computational perspectives on strategic reasoning, and identify explicit planning, grounded and faithful explanation, metacognitive calibration, and human--AI complementarity as directions for future research.

In this reproduction paper we investigate subliminal learning, a consequence of distillation where teacher models transmit behavioral preference traits through semantically unrelated data. The original paper explores two types of traits (animal preferences and misalignment), three data modalities (number sequences, code, and chain of thought), and several model families. We reproduce their experiments and extend the setup along three axes: new preference categories (actors and politicians), a new task (chess move generation), and an additional open-weight model (Ministral8B). We also run a controlled ablation on the numbers task's answer-space size (1-, 2-, and 3-digit sequences). We focus on open-weight models with accessible checkpoints on HuggingFace, since the original paper's GPT-4.x fine-tuning is no longer available. Our reproduction supports the original paper's claims, but our extensions show they are not universal as transmission strength varies across traits and tasks, and one model shows almost no effect at all.

Chess board recognition is the task of mapping the image of a chess board to the information of which piece is on which square. So far this task has two established benchmarks: ChessCog is synthetic, and ChessReD comes from smartphone pictures of a single chess board setup. We introduce ChessQueries, a new method combining a ViT encoder with a DETR-style decoder, which outperforms existing methods. On the ChessReD benchmark, we improve the state of the art from 15.3% to 99.2%, and demonstrate strong capabilities on out-of-distribution datasets. Our method saturates the task on the two datasets, with an average 0.01 wrong squares per board (vs. SotA: 3.4 / 0.15 respectively). We also share a new, harder public dataset, parsed from broadcasted top-level chess tournaments. Code, model weights and the SLCC data will be released.

Otter is a 15.3M-parameter human chess AI that predicts human move selection by modeling play as a time-aware, sequential process rather than treating each position in isolation. It combines two conditioning signals: (1) a move history encoder that conditions predictions on the last 20 moves, capturing opening preferences, positional drift, and intra-game behavioral tendencies; and (2) a time control module that modulates predictions based on clock pressure. Otter is trained on 6.1 billion positions from 117 million Lichess rapid games over 30 days on a single T4 GPU. Otter achieves 55.23% top-1 and 90.95% top-5 move-prediction accuracy, surpassing the prior state-of-the-art human chess model, Maia 2, with far fewer parameters and less training data. Across 11 Elo brackets (<1100 to >=2000), accuracy peaks at 57.38% in the 1900-1999 bracket. These results show that modeling chess as a time-aware, sequential activity yields more human-accurate move prediction than position-only approaches, using a smaller model. Code, trained models, and complete training logs are publicly released.

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.

Curling is often referred to as "Chess on Ice", owing to the tactical complexity of its decision-making process. Yet unlike chess, curling remains largely underexplored from a machine learning perspective, with prior work confined mainly to statistical approaches. We propose a reinforcement learning framework capable of quantitatively evaluating and comparing tactical options in curling. The game poses several modeling challenges: continuous state and action spaces, stochastic action outcomes reflecting player skill variability, and state transitions that are highly sensitive to small perturbations in the executed action. To address them, we employ the Deep Deterministic Policy Gradient actor-critic algorithm, adapted to exploit the finite-horizon structure of the game. Our experiments show that effective curling strategies can be acquired in a fully self-supervised manner, without any human-annotated data: on a reduced four-rock variant, the learned agent matches a hand-crafted expert heuristic in a regime where that heuristic is close to optimal, a parity we quantify against the intrinsic hammer advantage of the variant. Beyond the resulting policy, the learned critic provides a dense value estimate over the entire continuous action space, enabling the quantitative comparison of tactical alternatives for applications such as post-game performance analysis and decision support during athlete preparation.

Among chess opening positions that a strong engine judges essentially equal (Stockfish 18 evaluation within 10 centipawns of zero, depth-stable) and that humans actually reach on Lichess (October 2025; 1,661 positions, 16.1M occurrences), human results are not balanced. Positions carry outcome skews, each the gap between its games' actual results and what the players' ratings predict, whose directions are stable properties of the naturally-reached position: some positions favour White, others Black. These skews reproduce across three re-partitions -- disjoint player-account sets (primary), time, and disjoint rating bands -- and on an out-of-sample month eight months later. On the primary split, each position's skew is measured once in each account group, and the replication slope asks how well one measurement predicts the other after removing rating and opening-family effects: one means undiminished carry-over; zero, no linear relation. We find 0.69 (family-clustered 95% CI [0.65, 0.74]), rising to 0.94 on the most-popular, best-measured positions. The slope's value depends on the position mix. Existence is the invariant claim: it survives every tighter evaluation band, search depth, calibration, and popularity cutoff we test, and replicates within blitz and rapid separately. The typical skew is small (median $|δ| \approx 0.018$, about two percentage points of White score), yet it reproduces, position by position, across disjoint accounts. At these positions the disfavoured side also thinks longer. Even where the evaluation is most confident, it is not a sufficient statistic for human outcomes. The result is observational, and the causal question is left to a pre-registered randomised companion study.

Chess is a two player strategic game that is embedded in classical AI culture as it was once the frontier for intelligent behaviour. There was the silent assumption that the advent of computer engines that play better than the best humans will extinguish interest in the game. However, the opposite has come to pass, with a growing following for the game. A lot of the computational resources are now centered around training of players, where the engine output is just one aspect. Access to past games is also an essential part, both in knowing what games a specific player has played previously, and also which continuations at a certain position have led to victory more often for each of the two colour players. We present Chess_db a suite of logic programming tools that can effectively manipulate games both in memory and via creating back end databases. In particular, we provide versatile code that creates databases from PGN (portable game notation) game files and explore the suitability of open source key-value databases for storing position tables that provide near-instant access to information pertaining to substantially large number of games.

Latent, or silent, reasoning lets language models carry out intermediate computation in continuous vector space instead of words, and is widely assumed to function as an internal scratchpad the model consults during inference. Whether that assumption survives reinforcement learning has not been tested directly: existing causal analyses of latent reasoning are confined to math and logic tasks, comparing reliance on thoughts within one checkpoint, never before and after RL. We train a chess-playing model through a staged latent-reasoning curriculum followed by reinforcement learning, and find legality climbs monotonically to 61% (from a 48% pre-RL baseline) while checkmate confabulation is eliminated entirely. To locate this gain, we run a six-condition causal intervention suite on the same model before and after RL: substituting or noising the thought vectors leaves performance unchanged, ablating them costs only mild degradation, and only exact-zero vectors cause collapse. This robustness gap is itself the finding: under exact-zero corruption, legality collapses to 1% pre-RL versus 9% post-RL, a gap that survives correction across the full battery. A 10x-larger replication of the post-RL checkpoint's own battery confirms this: removing the thoughts, with or without restoring sequence length, also reaches significance; substitution and noise remain indistinguishable from baseline. RL appears to add robustness to disruption, not reliance on thought content. These results push back against the field's default assumption that latent thoughts function as an actively consulted inference-time scratchpad, and instead indicate latent reasoning's principal effect here is shaping the model's parameters during training. We also demonstrate a working RL gain in chess, where multiple groups report the same latent-reasoning-plus-RL recipe failing to improve accuracy over SFT.

Reinforcement learning (RL) has become central to improving large language models (LLMs) on complex reasoning tasks, yet RL post-training is largely studied in isolation from the pretraining that precedes it. As a result, two basic questions remain open: (1) how do pretraining choices (model size, data) shape the returns to RL compute, and (2) what does RL actually do to the model? These questions are difficult to study in the standard LLM setting: pretraining corpora are vast and uncontrolled, making it hard to attribute behaviors to pretraining versus RL, and systematic compute sweeps across both stages are prohibitively expensive. To address these challenges, we use chess as a controlled testbed for studying reasoning across the full pretraining-to-post-training pipeline. We follow the standard LLM training pipeline by pretraining language models from 5M to 1B parameters on human chess games, supervised fine-tuning on synthetic reasoning traces, and running RL on chess puzzles with verifiable rewards. Using this framework, we find that the post-RL performance at given RL compute level is well-predicted from the pretraining loss, and slope of the RL reward curves improves approximately linearly with the pretraining tokens. Beyond scaling, we find that RL does not simply sharpen the SFT policy: on easy puzzles it amplifies correct moves the SFT policy already preferred, while on hard puzzles it surfaces correct moves that were nearly absent under SFT. We further test whether our findings transfer beyond chess by training a 1B language model on math-domain text, where the same predictive pattern emerges: longer-pretrained checkpoints reach higher post-RL performance and improve faster under RL. In sum, we provide a quantitative account of the pretraining-to-RL interface and a controlled testbed for studying the science of reasoning across the full pretraining-to-post-training pipeline.

Chess engines have long achieved superhuman playing strength. However, the underlying strategy behind their move suggestions is difficult for human players, even skilled ones, to comprehend. Motivated by this, we propose the task of chess strategy verbalization, which is to describe chess strategies in natural language. We design (i) a pipeline for verbalizing strategies and (ii) an evaluation framework for objective evaluation of generated strategy descriptions. Our experiments show that natural language is a promising and interpretable medium for communicating strategic information to both human and LLM players. We glean additional interesting insights, including (a) the importance of evaluating strategies beyond the main line, (b) the limitations of pure concept-based descriptions, and (c) the limitations of relying on LLMs rather than humans for evaluation.

Rating systems such as Elo serve as the gold standard for matchmaking in competitive chess. However, they inherently suffer from response lag due to their exclusive reliance on match outcomes, neglecting the granular quality of gameplay. Nevertheless, incorporating move-by-move information into rating adjustments presents a significant challenge given the substantial noise and the vastness of the game-state space. To address this, we propose the Drift-Diffusion-Enhanced Elo Rating System (DD-Elo), a novel skill assessment framework inspired by the drift diffusion model (DDM) from cognitive neuroscience. By modeling skill expression as a decision-making process, our model integrates move-level data to capture rapid skill fluctuations. We provide a rigorous mathematical derivation proving that DD-Elo maintains a bounded deviation from the traditional Elo system, ensuring theoretical alignment. Extensive experiments demonstrate that DD-Elo adapts to skill changes faster than Elo. Our findings suggest that DD-Elo offers an explainable, highly responsive, and backward-compatible solution for chess rating ecosystems. The implementation code is publicly available at https://github.com/Aquila-zhou1/DD-Elo .

Chess engines have evolved from search-based systems optimized solely for strength to neural policies capable of modeling human decisions across much of the rating spectrum. Maia-3, the strongest human-like move policy for chess, models the typical moves of a given rating but does not model high Elo strength well (2500+ Lichess Elo) nor has an extensible architecture for modeling individual play style. On the other hand, search-based engines like Stockfish are far stronger than any known human but struggle to model human-like play. To solve these problems, we present Matilda, a permutation-invariant set transformer that re-ranks the full legal-move distribution produced by a frozen Maia-3 and improves it along both dimensions with one 1.7M-parameter model. Matilda uses Maia-3 to provide both global context and search candidates. Context is encoded from Maia-3's hidden representation, time control, and an optional 32-dimensional player-style vector, while the top-16 candidate moves are optionally rescored by Stockfish. A zero-initialized head scatters per-candidate adjustments back into the policy logits, so the untrained model is exactly Maia-3 and every gain is value-added under full-vocabulary NLL. On a 2500+ Elo benchmark from Lichess, Matilda improves on Maia-3 by +0.5-0.6% below 2800 but +4.3%, +11.9%, and +21.9% at 2800-2900, 2900-3000, and 3000+, respectively, and an additional +0.41% overall from player-style embeddings. Ablations show that the improvements are primarily driven by the engine-derived features, the mechanism is not engine-specific, and the gains survive memorization, sibling, and account audits while preserving Maia-3 at 1000-2500 Elo. Because search supervision is modular, Matilda naturally supports interchangeable search engines, demonstrated by replacing Stockfish with an AlphaZero-family engine.

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.

Multi-party dialogue is a critical setting for studying collaborative reasoning and decision-making, yet existing datasets rarely focus on structured, in-depth complex reasoning tasks. We introduce DeliChess, a novel dataset of group deliberation dialogues in which participants collaboratively solve multiple-choice chess puzzles. Each group first completes the puzzle individually, then engages in a multi-party discussion before submitting a revised collective answer. The dataset includes 107 dialogues with full transcripts, pre- and post-discussion choices, and metadata on puzzle difficulty and move quality. We evaluate performance using three metrics based on chess engine evaluations, and find that deliberation significantly improves group accuracy. We further analyse the role of probing utterances (i.e., messages that elicit proposals, justifications, or strategic reflection) using a classifier trained on prior deliberation data. While probing makes group performance more variable after discussion, it does not consistently lead to better performance. Our dataset offers a rich testbed for modelling group reasoning, dialogue dynamics, and the resolution of differing perspectives and opinions in a well-defined strategic domain.

We present ChessMimic, a system of three small encoder-only transformers - for move, thinking-time, and outcome prediction - conditioned on the position, recent move history, player rating, and clock state. We fit a separate instance of each model per 100-Elo rating band, trading parameter efficiency for sharper per-skill calibration. On a held-out month-wide slice of Lichess Rated Blitz games ChessMimic's human move prediction accuracy outperforms Maia-2 in every Elo band. Compared to Maia-3, our 9M parameter model's accuracy sits between Maia-3-5M and Maia-3-23M without the additional complexity of Geometric Attention Bias. In addition to the move matching model, we also train a game outcome model that conditions not only on the position, but also player ratings, time control, and remaining clock times. The outcome model achieves an AUC of 0.78 out of sample, beating Maia-2 as well as logistic regressions based on material, ratings, and clock time. Finally, we train a clock model that predicts human thinking times. The clock model provides a usable but non-SOTA per-ply think-time signal under ALLIE-style filters (Pearson r = 0.41, Spearman rho = 0.50, MAE 4.10 s, against ALLIE's reported r = 0.70), with the residual gap concentrated in per-position bucket sharpness rather than bucket-marginal calibration. A public demo is at 1e4.ai and we release code, per-band weights, and the C++ data-filter pipeline code in GitHub.

Combinatorial and optimization problems are fundamental to many industrial AI applications. Solving large-scale real-world instances of such problems typically requires careful problem formalization, specialized solvers, and expert-designed heuristics. Thus, experts need to specify not only what solutions are, but also how they are derived. By introducing the tool CHECKMATE, we show that algorithm generation via code evolution represents a paradigm shift by eliminating the need to formulate the how. CHECKMATE solely relies on the what. Specifically, a formal specification ensures solutions' correctness and enables systematic performance evaluation of the generated programs, while a natural language description guides the evolutionary process. The effectiveness of our method is demonstrated on selected problems from two industrial domains: configuration and scheduling. In all cases, the evolved algorithms consistently outperform state-of-the-art solvers. This underscores the potential of formal methods in guiding code evolution for automatically solving complex real-world problems.

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.

Recent advances in large language models have enabled natural language to serve as a flexible interface for controlling complex systems, but often at the cost of large-scale multimodal training or weakened domain-specific inductive biases. In structured decision-making domains such as chess, specialized policy networks achieve strong performance but lack semantic controllability, while prompt-conditioned language models are more flexible yet typically exhibit weaker domain grounding. We propose $\textbf{UniMaia}$, a framework for prompt-conditioned policy modulation that adapts a frozen Lc0-based chess policy network using a parameter-efficient text encoder and a ControlNet-style conditioning mechanism. UniMaia enables semantic control over gameplay, including opening selection and player strength, while preserving the pretrained policy representations. We further introduce $\textbf{UniMaia-Aux}$, which incorporates auxiliary temporal conditioning and behavioral prediction objectives. To support this work, we construct a large-scale metadata-augmented Lichess dataset, develop a semi-automated prompt-generation pipeline, and introduce benchmarks spanning both prompt-conditioned and metadata-conditioned settings. UniMaia achieves state-of-the-art expected accuracy on several prompt-conditioned benchmarks and competitive top-move accuracy on general instruction-following tasks, while remaining competitive with dedicated metadata-conditioned approaches on human move prediction benchmarks. UniMaia-Aux further improves expected accuracy and behavioral modeling across several evaluation settings, with modest trade-offs in top-move accuracy. Overall, our results demonstrate that prompt-conditioned control of domain-specific policy networks is feasible without end-to-end multimodal training, while highlighting trade-offs between controllability and predictive performance.

Chess has long served as a canonical testbed for artificial intelligence, but modeling approaches for its central tasks have diverged. Maximizing playing strength, predicting human play, and enabling interpretability are typically solved with disparate architectures, and these designs are often misaligned with the geometry of the domain. This raises the natural question of whether these objectives require separate modeling paradigms, or if there exists a single architecture that supports them simultaneously. We introduce Chessformer, a unified architecture that advances the state of the art on all three central goals in chess modeling. Chessformer is an encoder-only transformer that represents board squares as tokens, augments self-attention with a novel dynamic positional encoding called Geometric Attention Bias (GAB) that adapts to domain-specific geometry, and predicts actions with an attention-based source-destination policy head. We evaluate Chessformer on each front. First, we develop \maiathree, a family of models for human move prediction that reaches 57.1% move-matching accuracy, significantly surpassing the previous state of the art with fewer than a quarter of the parameters. Second, we integrate Chessformer into Leela Chess Zero, a leading open-source engine, adding over 100 Elo of playing strength and resulting in tournament victories over Stockfish in major computer chess competitions. Third, we show that Chessformer's square-token design makes attention patterns and activations directly attributable to board squares, enabling granular interpretability analyses that prior architectures do not naturally support. More broadly, our results demonstrate that aligning a model's tokenization, positional encoding, and output design with the underlying structure of a domain can yield simultaneous gains in performance, human compatibility, and interpretability.

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.

Watermarking techniques for large language models (LLMs), which encode hidden information in the output so its source can be verified, have gained significant attention in recent days, thanks to their potential capability to detect accidental or deliberate misuse. Similar challenges involving model misuse also exist in the context of game-playing, such as when detecting the unauthorized use of AI tools in gaming platforms (e.g., cheating in online chess). In this paper, we initiate the study of how game-playing strategies can be watermarked. We show how the KGW watermark for LLMs can be adapted to watermark game-playing agents in perfect-information extensive-form games. The watermark can then be detected using a statistical test. We show that the degradation in the quality of the watermarked strategy profile, quantified by the expected utility, can be bounded, but there is a tradeoff between detectability and quality. In our experiments, we bootstrap the watermarking framework to various chess engines and demonstrate that a) the impact of the watermark on the quality of the strategy is negligible and b) the watermark can be detected with just a handful of games.

While artificial intelligence has achieved superhuman performance in chess, developing models that accurately emulate the individualized decision-making styles of human players remains a significant challenge. Existing human-like chess models capture general population behaviors based on skill levels but fail to reproduce the behavioral characteristics of specific historical champions. Furthermore, the standard evaluation metric, move accuracy, inherently penalizes natural human variance and ignores long-term behavioral consistency, leading to an incomplete assessment of stylistic fidelity. To address these limitations, an architecture is proposed that adapts the unified Maia-2 model to champion-specific embeddings, further enhanced by the integration of a limited Monte Carlo Tree Search (MCTS) process to enrich tactical exploration during move selection. To robustly evaluate this approach, a novel behavioral metric based on the Jensen-Shannon divergence is introduced. By compressing high-dimensional board representations into a latent space using an AutoEncoder and Uniform Manifold Approximation and Projection (UMAP), move distributions are discretized on a common grid to compare behavioral similarities. Results across 16 historical world champions indicate that while integrating MCTS decreases standard move accuracy, it improves stylistic alignment according to the proposed metric, substantially reducing the average Jensen-Shannon divergence. Ultimately, the proposed metric successfully discriminates between individual players and provides promising evidence toward more comprehensive evaluations of behavioral alignment between players and AI models.

While researchers are finding concepts represented as linear directions in language models, a bag of linear directions fails to capture relational structure. To better understand this dichotomy, we study a model with known linear representations, but trained in a highly structured domain -- the board game Othello. While the model's internal board-state representation is linearly decodable, we find additional structure in the form of tensor product representations (TPRs). We train TPR probes to recover shared structure amongst the linear probes, yielding a factorization into square-embeddings, color-embeddings, and a binding matrix that composes them to construct the model's board-state representation. We find geometric signatures within the weights of our TPR probe that align with the structure of the board, but perhaps more importantly, that the linear probes can be recovered directly from the parameters of our TPR probe. Our findings suggest that directional representations may be projections of more structured underlying representations.

Constraint Programming (CP) is a powerful paradigm for solving combinatorial problems, yet translating natural language problem descriptions into executable models remains a significant bottleneck. While Large Language Models (LLMs) show promise in automating this translation, they often struggle with subtle semantic errors in the absence of oracle validation at test time. To address this, we introduce CP-SynC (Constraint Programming modeling with Synthesized Checkers), a multi-agent workflow for zero-shot constraint modeling in MiniZinc. CP-SynC coordinates modeling agents that generate and refine candidate models and validation agents that synthesize semantic checkers to provide feedback on semantic correctness. To mitigate noise inherent in individual LLM outputs, CP-SynC explores multiple modeling trajectories in parallel and employs selection agents to select the final model via multi-agent evidence aggregation. Extensive experiments on a benchmark of 100 CP problems show that CP-SynC substantially outperforms existing baselines in MiniZinc modeling.

Backdoor attacks threaten the deep learning supply chain by poisoning a small fraction of the training data so that a model behaves normally on clean inputs but misclassifies trigger-carrying inputs to an attacker-chosen target class. Clean-label backdoor attacks are especially dangerous because poisoned samples remain label-consistent and are therefore harder to detect. Yet existing clean-label attacks typically rely on expensive optimization, surrogate-model training, or nontrivial data access. We present Checkerboard, a theoretically grounded, learning-free clean-label backdoor attack that is effective, efficient, and simple to implement. From a linear separability formulation, we derive a checkerboard trigger in closed form, removing the need for surrogate-model training and trigger optimization. For texture-rich datasets, we introduce Complexity-driven Sample Selection, which uses only target-class data to improve trigger-to-background contrast by selecting low-complexity images for poisoning. Across four benchmark datasets, Checkerboard outperforms 8 baseline attacks and achieves state-of-the-art performance under low poisoning budgets. For example, on CIFAR-10, under a trigger perturbation budget of $10/255$, poisoning 20 training samples achieves $99.99\%$ Attack Success Rate (ASR). On ImageNet-100, a poisoning rate of only $0.46\%$ yields over $94\%$ ASR without degrading clean accuracy. The proposed attack also remains effective against state-of-the-art backdoor defenses and shows strong resistance to adaptive defenses.

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.

Human-AI collaboration often requires dividing complex tasks into complementary subtasks. As a task unfolds, users may want to shift which subtasks they perform and which their AI partner performs, in response to evolving task demands and perceptions of the AI's capabilities. In this work, we investigate whether behavioral signals can reveal such changes during a sequential decision-making task. We conducted a study using hand-and-brain chess, where, on each turn, participants chose either to select the piece type (brain) while their AI partner chose the move (hand), or to choose the move after the AI selected the piece type. Across 21 chess players, this yielded more than 1,100 decisions to retain their role from the previous turn or switch to the other role. Players generally retained their current roles across turns. When participants did switch, they exhibited more exploratory gaze patterns and role switches were associated with lower subsequent move quality. Using these behavioral and task-specific signals, we trained a classifier to distinguish switch from stay decisions, achieving a PR-AUC of 0.56 (compared to a random baseline of 0.39). Feature-set ablations showed that gaze and task-specific features contributed most to model performance. Role switching was not a simple choice between controlling and delegating the task as both roles required participants to perform one subtask and delegate the other. However, interviews showed that many participants perceived selecting the piece type as giving them greater control. Perceived AI ability, relative subtask difficulty, and desired influence over the direction of play shaped these role preferences. These findings suggest that behavioral cues could help intelligent systems recognize when users want to reallocate complementary responsibilities during collaboration.

The advent of artificial intelligence has propelled AI-Generated Game Commentary (AI-GGC) into a rapidly expanding research area, offering advantages such as scalable availability and personalized narration. However, existing studies remain fragmented, and a systematic survey that unifies prior efforts is still lacking. To bridge this gap, our survey introduces a unified framework that systematically organizes the AI-GGC landscape. We present a novel taxonomy focused on three core commentator capabilities: Live Observation, Strategic Analysis, and Historical Recall, and further categorize commentary into three corresponding types: Descriptive Commentary, Analytical Commentary, and Background Commentary. Building on this structure, we provide an in-depth review of methods, datasets, and evaluation metrics, analyzing their strengths and limitations. Finally, we highlight key challenges and point out promising directions for future research in AI-GGC.