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.
Figures & tables
Figure 1: Chess engines play strong moves but can’t explain them. Frontier/finetuned LMs give plausible explanations, but are limited by weak play. Queen offers the best of both worlds.
Figure 2: We use an encoder-decoder architecture inspired by Flamingo ( Alayrac et al., 2022 ) . The encoder is an Lc0 chess network, and the decoder is an instruction-tuned language model. The k -th layer embeddings of Lc0 flow into a Flamingo block injected before the 2k -th LM layer, and all previously trained parameters are frozen during domain adaptation.
Figure 3: An example explanation generated by Queen , snipped for readability. The explanation consists of natural language prose (green) followed by a best move and PV prediction (blue).
Figure 4: Domain adaptation progressively teaches the model to extract static features in the current board state ( static-current ), reason about available moves and interactions ( dynamic-current ), reconstruct a future board state from move sequences ( static-future ), and finally reason about the resulting position ( dynamic-future ).
Figure 5: We repeatedly distill the search-consolidated explanations back into the model for iterative self-improvement. Analogous to the Bellman update, a consolidated explanation combines the explanations at child nodes to explain why one move is the best and the shortcomings of other moves.
Model
Elo
Queen (ours)
2697
Gemini
2201
Sol
2071
Luna
1822
C1-4B
514*
Median Grandmaster
2730
Table 1: Estimated ratings anchored to Lichess Elos after 32 games. All frontier models use high reasoning effort. *C1-4B lost all 32 games.
Model
Tactical ↑
General ↑
NMR (%)
FNMR (%)
NMR (%)
FNMR (%)
Queen
68.8
91.6
66.6
97.1
Gemini
66.9
82.5
63.0
89.0
Sol
65.1
81.9
61.5
86.8
Luna
35.6
53.5
47.1
73.6
C1-4B
—
43.2
—
38.8
Table 2: Substantiation evaluation on 1,000 tactical and 1,000 general positions. NMR is the fraction of predicted PVs containing no mistakes; FNMR is the fraction of positions in which the model’s predicted best move is not a mistake. All frontier models use high reasoning effort. Queen performs the best across all metrics on both tactical and general positions.
Model
Structural Coherence
Conceptual Coherence
Fluency
Queen
3.51
2.76
4.45
Gemini
3.55
3.30
4.98
Sol
3.51
3.61
4.99
Luna
2.82
2.94
4.96
C1-4B
2.48
2.16
4.94
Table 3: Evaluation of the various models on coherence and fluency. Frontier models use high reasoning effort. All models are fluent in their output. Gemini obtains the best structural coherence, though Queen and Sol obtain comparable scores. Queen struggles with conceptual coherence, as iterative search-distillation cannot teach it to verbalize and describe motifs it hasn’t seen.
Model
Elo ↑
Tactics ↑
Pawn -1
1782
73.9
− Encoder
514 ∗
9.7
− Curriculum
514 ∗
1.3
Table 4: Ablations of Queen evaluated after Sol -seeding. Both the encoder and curriculum are essential for a good initialization.
Outcome
Rate (%)
Agrees with Lc0
46.2
Disagrees, in top-5
39.1
Outside top-5
14.7
Table 5: Queen disagrees with Leela on 53.8% of positions with five or more reasonable moves, suggesting that it does not simply reproduce Leela’s policy head.
Model
Elo ↑
P1
P2
P3
P4
Queen
1782
2024
2187
2346
Queen (HCE)
2115
2432
2476
2497
Table 6: Performance of Queen with and without frontier-model distillation. The HCE variant uses an alternative data construction pipeline based on Stockfish’s hand-crafted evaluation.
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
Question task
Sample Q → A / answer clause
Stages 1 & 3 — Static Board Understanding
Identify the piece on a queried square
What piece is on <SQUARE_28>? → There is <PIECE_MN> on <SQUARE_28>.
Locate all squares holding a queried piece
Where is <PIECE_MR>? → <PIECE_MR> occupies <SQUARE_1> and <SQUARE_8>.
List pieces on a queried file
Pieces on file <SQUARE_5>--<SQUARE_61>? → 1 <PIECE_MP> and 1 <PIECE_OK>.
List pieces on a queried rank
Pieces on rank <SQUARE_1>--<SQUARE_8>? → Walking the rank: …
List pieces on a queried diagonal
Pieces on diagonal <SQUARE_1>--<SQUARE_64>? → …(or ‘‘open diagonal’’)
Appendix
Table 7: Question types used for our four-stage domain adaptation.
Data source
curr-static
curr-dynamic
future-static
future-dynamic
Stage-1 data
100%
–
–
–
Stage-2 data
10%
90%
–
–
Stage-3 data
6%
8%
86%
–
Stage-4 data
6%
6%
8%
80%
Appendix
Table 8: Data composition of the four stages of domain adaptation training. Rows and columns correspond to the final stage data mixture and data sources described above. Earlier-stage data is replayed at a small proportion to prevent forgetting.
Hyperparameter
Value
Training steps
stage 1
50K
stage 2
60K
stage 3
30K
stage 4
100K
Bridge learning rate
Appendix
Table 9: Training hyperparameters for the four-stage curriculum. Hyperparameters shared across all stages are listed once.
Static
Dynamic
Current
Future
Current
Future
0.9997
0.9997
0.9897
0.9607
Appendix
Table 10: Held-out test set accuracies of our model.
Static
Dynamic
Architecture
Model family
Current
Future
Current
Future
Flamingo
SmolLM3
99.97
99.97
98.97
96.07
Qwen3
99.80
99.87
98.42
96.83
Gemma3
99.04
98.51
95.47
79.78
LLaVA
SmolLM3
99.80
99.80
99.00
93.20
Qwen3
99.93
99.89
97.20
57.20 ∗
Appendix
Table 11: Architecture × Model-family ablation: Accuracy (%) on Static and Dynamic on held-out validation sets. ∗ Undertrained: the training run was aborted early, at step counts matched to Flamingo.
Hyperparameter
Value
Training examples
8,402
Validation examples
200
Training steps
2,100
Effective batch size
16
Maximum sequence length
2,048
Bridge learning rate
1×10−5
Appendix
Table 12: Supervised fine-tuning hyperparameters for distillation from GPT-5.6-Sol (low).
Hyperparameter
Value
Training examples
150K–285K
Maximum training steps
30K
Effective batch size
32
Maximum sequence length
2,048
Bridge learning rate
1×10−4
Decoder learning rate
1×10−5
Appendix
Table 13: Supervised fine-tuning hyperparameters for one self-distillation iteration. Each iteration initializes from the selected checkpoint of the preceding iteration.
Opponent
Search budget (nodes)
Anchored Elo
Stockfish
10
1978
Maia-2200 (Lc0)
1
2037
Stockfish
100
2085
TinyGyal-8 (Lc0)
10,000
2422
Stockfish
1,000
2597
11258-16x2-se-4 (Lc0)
10,000
2689
Appendix
Table 14: The opponents we use for accuracy evaluations in Section 4.1 .