Language Models that Play Chess and Explain Their Moves

AI summary

Overview

Research area: Natural Language Processing, specifically domain adaptation of language models to chess and the generation of natural-language explanations grounded in strong play.

Technical level: Intermediate. The paper assumes familiarity with encoder-decoder architectures, cross-attention, supervised fine-tuning, and chess engine terminology such as centipawns and principal variation. The high-level argument is accessible, but the training recipe and evaluation design involve several moving parts.

Scope: The paper introduces Queen, a 4B-parameter chess-language model that pairs a silent chess encoder with an instruction-tuned language model decoder and is refined through an iterative search-distillation loop, then evaluates its move accuracy (Elo), principal-variation quality, and explanation coherence against frontier models and a similarly sized prior system.

What This Paper Is About

Chess engines play at a superhuman level but produce no natural-language reasoning, while language models can write fluent explanations but play chess weakly, which limits how useful those explanations are. The paper asks whether a single model can both play at Grandmaster level and explain its moves in prose. The authors build Queen to close that gap by giving a language model direct access to the internal representations of a strong chess encoder, then repeatedly distilling improved, search-consolidated explanations back into the model.

Key Contributions

1. An encoder-decoder architecture and training recipe for adapting language models to chess. A 240M-parameter Lc0 BT5 chess encoder ("Leela") is connected to an instruction-tuned LM decoder (SmolLM3-3B) through gated cross-attention layers, with a curated question-answering curriculum used to teach the decoder to extract chess concepts from the encoder's hidden states. The authors state the pipeline is general and can extend to any setting where a domain-expert Transformer encoder can be trained.

2. An iterative search-distillation algorithm. Inspired by the Bellman value update, the method analyzes positions after the model's top candidate moves, consolidates them into an explanation of the current position, and distills that explanation back into the model. The authors note it is general and extendable to domains benefiting from tree-search methods such as MCTS and alpha-beta pruning.

3. An evaluation framework for explanation quality along three dimensions. The framework separates accuracy (quality of move recommendations, measured through full-game Elo), substantiation (whether predicted principal variations are mistake-free), and coherence (structural, conceptual, and fluency quality judged by an LM).

4. A model, Queen, and supporting releases. Queen reaches an estimated 2697 Elo with explanations that the authors describe as fluent and approaching GPT-5.6-Sol in coherence. The paper links to models, code, and a website.

Main Findings

• Playing strength far exceeds frontier language models. Queen reaches an estimated rating of 2697 after 32 games per model against 8 engines of varying strengths, anchored to the Lichess Elo scale. Gemini-3.1-Pro scores 2201, GPT-5.6-Sol 2071, GPT-5.6-Luna 1822, and C1-4B 514 (it lost all 32 games). Queen beats Sol by over 600 rating points and Gemini by over 450, corresponding to 97.4% and 94.6% expected win rates respectively.

• Iterative distillation drives the gains. Over seven iterations Queen gains 915 Elo points: 1782 → 2024 → 2187 → 2346 → 2539 → 2434 → 2559 → 2697. The authors' abstract describes this as "over 900 Elo points (1782 → 2697)."

• Queen remains below its own encoder. The Leela (BT5 encoder) is listed at 2987 Elo. The authors characterize the gap between Queen and Leela as a form of "verbalization debt" — the difficulty of expressing latent expert knowledge in language.

• Comparison to human titles. For context, the paper lists median Grandmaster at 2730, median International Master at 2560, and median FIDE Master at 2470 on the Lichess blitz scale, and notes there are 1,899 Grandmasters as of October 2, 2026, fewer than 0.01% of active online players.

• Best substantiation across all metrics. On 1,000 tactical puzzles (projected Lichess difficulties 609 through 2905) and 1,000 general positions drawn from human games, Queen scores the best no-mistake rate (NMR) and first-move no-mistake rate (FNMR) on both sets: 68.8% / 91.6% on tactical puzzles and 66.6% / 97.1% on general positions. Gemini follows at 66.9% / 82.5% and 63.0% / 89.0%; Sol at 65.1% / 81.9% and 61.5% / 86.8%; Luna at 35.6% / 53.5% and 47.1% / 73.6%; C1-4B reports only FNMR at 43.2% and 38.8%. Queen beats Gemini by 2 points on NMR and 9 points on FNMR.

• Coherence is mixed, with a specific weakness. Under a GPT-5.6-Sol (high) judge on a 1–5 Likert scale, Queen scores 3.51 structural coherence, 2.76 conceptual coherence, and 4.45 fluency. Gemini scores 3.55 / 3.30 / 4.98, Sol 3.51 / 3.61 / 4.99, Luna 2.82 / 2.94 / 4.96, and C1-4B 2.48 / 2.16 / 4.94. All models are fluent. Queen ties Sol on structural coherence and approaches Gemini; its low conceptual coherence score is attributed to hallucinations of motifs and patterns that can propagate through consolidation.

• Queen analyzes more lines than the judge's comparison point. Queen considers an average of 30.0 ply in its entire analysis, while Sol considers 23.8 ply, which the authors suggest gives the judge more opportunity to penalize Queen.

• Both the encoder and the curriculum matter. Ablations evaluated immediately after the Sol-seeding stage: Pawn-1 reaches 1782 Elo and 73.9 on tactics; removing the Leela encoder drops to 514 Elo and 9.7; removing the domain-adaptation curriculum drops to 514 Elo and 1.3. Both variants are marked with an asterisk.

• Queen does not simply copy Leela's policy head. On 1,000 positions where at least five moves have expected win rates within 3% of the Stockfish-optimal move, Queen agrees with Lc0 on 46.2% of positions, disagrees but keeps its move in Lc0's top-5 on 39.1%, and is outside the top-5 on 14.7% — disagreeing on 538 of the 1,000 positions.

• Frontier-model seeding is not strictly necessary. A variant trained instead on templatic explanations derived from Stockfish's hand-crafted evaluation (HCE) follows a similar Elo trajectory (2115 → 2432 → 2476 → 2497 across iterations P1–P4) compared with Queen's 1782 → 2024 → 2187 → 2346 over the same iterations.

• Architecture choices were ablated. The Flamingo-style bridge contains about 470M parameters; a LLaVA-style prefix-token projection with LoRA (rank 16 on Q/K/V/O) contains about 83M trainable parameters; a direct KV-cache projection contains about 612M trainable parameters and trailed Flamingo and LLaVA by roughly 5–10 percentage points across every learning-rate and dataset configuration on Static questions, so it was dropped. Decoder ablations compared SmolLM3-3B, Qwen3-4B, and Gemma3-4B.

• Domain-adaptation accuracy is high. Held-out test accuracies are 0.9997 (Static-Current), 0.9997 (Static-Future), 0.9897 (Dynamic-Current), and 0.9607 (Dynamic-Future).

Methodology in Plain English

The authors start from the observation that two kinds of systems already exist and each is missing half of what they want. Chess engines like the Lc0 BT5 network (Leela) hold rich internal representations of board positions but only output move policies and win/draw/loss probabilities. Language models produce fluent text but play chess poorly. Rather than hoping a language model will learn chess concepts from expert game records, the authors connect the language model directly to a model whose representations already encode those concepts.

The connection is done the way vision-language models connect an image encoder to a text decoder. The authors borrow the Flamingo design: trainable gated cross-attention layers sit between the decoder's normal layers. Keys and values come from encoder hidden states; queries come from decoder hidden states. Instead of using only the encoder's final hidden state, they pair encoder layer i with decoder layer 2i and insert the cross-attention layer before the 2i-th decoder block, so the decoder can draw on earlier and multi-scale board features. A tanh gate initialized to zero means cross-attention starts as a no-op and opens gradually. The encoder and decoder are frozen during domain adaptation; only the bridge and new token embeddings train.

The bridge is taught to interpret the encoder through a four-stage question-answering curriculum. Questions concern either the current position or a future position reached by a sequence of 1 to 8 moves, and fall into four categories: Static-Current (which piece is on a square, where a piece is, pieces on a file/rank/diagonal, piece counts, material points), Dynamic-Current (legal moves for a piece, attackers and defenders, available captures and checks, ways out of check, whether a position is checkmate), Static-Future (reconstruct the board after a move sequence, then answer a static query), and Dynamic-Future (same reconstruction plus dynamic reasoning about the resulting position). Each question type has three query-and-answer formats for diversity, and all answers are generated and verified programmatically. Positions come from the public Lichess dataset. The stages are trained sequentially (Static-Current → Dynamic-Current → Static-Future → Dynamic-Future) with earlier-stage data replayed at low proportions to prevent forgetting. Because the tokenizer handles square names inconsistently and words like "bishop" and "knight" carry non-chess meanings in pretrained embeddings, dedicated tokens are added for all 64 squares and 12 piece types. Training uses AdamW with a cosine learning-rate schedule, bf16 precision, an effective batch size of 256, 5% warmup, a final-to-peak LR ratio of 5%, and early stopping; steps are 50K / 60K / 30K / 100K across the four stages, with bridge learning rates of 1e-4 / 8e-5 / 7.5e-5 / 2e-4 and token embedding learning rate at 0.1× the bridge rate. The resulting checkpoint is called Pawn (Position AWare Network).

Pawn can answer structured questions but has not seen the target explanation format, so the authors seed it with examples from GPT-5.6-Sol (low). They source 15,000 positions from Lichess games and puzzles, prompt Sol for a best move, a principal variation, natural-language prose, three promising moves, and a position evaluation, filter out responses with illegal moves or mistakes, and fine-tune to get Pawn-1.

From there, the training loop mirrors AlphaZero's pattern of generating improved targets with search and distilling them back, but in natural language. Each iteration from Pawn-k to Pawn-(k+1) has five steps: Sample about 400K root positions from games between the current checkpoint and Stockfish at various node counts, human Lichess games, and mined Lichess puzzles; Generate an explanation with three promising moves from Pawn-k, replacing the worst move with the Stockfish oracle move if all three are mistakes (a mistake is a 10% or greater drop in expected win rate versus the Stockfish oracle) and generating explanations for the three resulting child positions; Recurse into a child when its best-move prediction is a mistake, discarding the root and other children, until all three children are mistake-free or a maximum depth is reached; Consolidate the three child explanations with Qwen3.8-27B, instructed to introduce no new content; and Train after filtering, comparing the consolidated and original principal variations at their first divergence and discarding consolidated explanations whose move is illegal or has a worse Stockfish evaluation. Seven iterations are run, and Pawn-8 is renamed Queen.

Evaluation splits into three questions. For accuracy, the model plays 32 full games against a set of 8 engines of varying strength, and ratings are reported anchored to the Lichess Elo scale using the known strength of the Leela networks. For substantiation, the model produces principal variations on 1,000 tactical puzzles and 1,000 general human-game positions, scored by no-mistake rate and first-move no-mistake rate. For coherence, a GPT-5.6-Sol (high) judge scores structural coherence, conceptual coherence, and fluency on a 1–5 Likert scale.

Why This Matters

Impact on research. The paper offers a general recipe rather than a chess-specific trick: pair a language model with an existing silent expert encoder via cross-attention, teach the bridge with a staged QA curriculum, then improve reasoning by consolidating and distilling search-derived analyses in natural language. The authors explicitly frame the iterative algorithm as a natural-language analogue of the Bellman update and note it applies to any stateful environment that benefits from tree search. The result also quantifies the "verbalization debt" between a model's internal competence (Leela at 2987 Elo) and its stated recommendations (Queen at 2697 Elo), which is a useful framing for anyone trying to make expert systems explain themselves. The finding that a Stockfish-HCE-derived templatic dataset produces a similar Elo trajectory suggests frontier-model distillation is not a prerequisite.

Real-world applications:

• Chess coaching and study tools. A model that recommends a move, gives the principal variation, and explains why alternatives are worse addresses the two failure modes of existing tools: engines that do not explain, and language models whose weak play makes their explanations unreliable.
• Post-training data generation. The paper notes that good explanations can serve as valuable post-training data for language models, so the pipeline can feed forward into other training runs.
• Domain-specific assistants where a silent expert already exists. The authors name games, robotics, and computer use as settings where a strong encoder produces representations but no language, making the same bridge-plus-curriculum pattern applicable.
• Human-like training opponents and teaching tools. The paper situates itself alongside human-aligned engines such as Maia and Allie, which predict moves human players of a given skill level would make; adding natural-language reasoning extends that teaching function.

Industry relevance. The result is a demonstration that a 4B-parameter model can outperform frontier systems with "three orders of magnitude fewer parameters" on a specific domain, which matters for cost-sensitive deployment of domain assistants. The authors also flag that frontier models' substantial computational cost limits their practicality for this task.

Future Directions

1. Raising conceptual coherence. Queen scores 2.76 on conceptual coherence, far below its 3.51 structural coherence and 4.45 fluency. The authors attribute this to hallucinations of motifs and patterns that can propagate through consolidation and call it a limitation of the method, looking to future work to resolve it.

2. Extending beyond chess. The architecture and training procedure are described as general; the natural next step is applying them to other domains with silent expert encoders, including games, robotics, and computer use.

3. Reducing or removing dependence on frontier-model seeding. The HCE variant shows a similar Elo trajectory without Sol-seeded data, leaving open how far the templatic-data route can be pushed and how it compares at later iterations.

4. Direct comparison with concurrent encoder-decoder work. The authors state they would also like to compare against LLAMIA, concurrent work with a similar architecture, but its models had not been released as of writing.

Target Audience

Researchers and engineers working on domain adaptation of language models, encoder-decoder and cross-attention architectures, and explanation generation would benefit most, along with those interested in games as a testbed for machine intelligence. The paper is also relevant to chess players and tool builders who want model output that is both strong and interpretable, and to practitioners in robotics or computer use who have access to a strong but silent domain expert and want a language interface on top of it. Readers need enough background to follow cross-attention, fine-tuning, and chess engine terminology such as principal variation and centipawns; the paper's own framing assumes familiarity with prior work on AlphaZero, Lc0, and vision-language model bridges.

Authors’ abstract

Modern chess engines are silent experts: they play at a superhuman level, but do not offer explanations for their play. On the other hand, language models (LMs) can generate plausible-sounding explanations, but their weak playing strength limits the utility of their explanations. We introduce Queen, a 4B-parameter chess-language model that can explain its moves and plans while playing at the level of a typical Grandmaster. Our novel framework enables domain-specific reasoning through complementary components: an encoder-decoder architecture and an iterative distillation algorithm. This architecture integrates a silent expert chess encoder with an instruction-tuned LM through cross-attention, which we train via a question-answering curriculum to extract chess concepts from the encoder's representations. Building on this domain-adapted model, we iteratively improve its explanations with a natural-language analog of the Bellman update: the model analyzes the positions after its top candidate moves and consolidates them into an explanation of the current position, which is then distilled back into the model. Over seven iterations, our model gains over 900 Elo points (1782 to 2697), substantially surpassing all frontier models on both playing strength and puzzle accuracy, despite containing three orders of magnitude fewer parameters. Furthermore, LM-based evaluations show that our explanations are fluent and approach GPT-5.6-Sol (high) in coherence. The generality of our architecture and training procedure suggests a recipe for applying language models to domains where silent expert encoders are available, like games, robotics, and computer use.