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arXiv:2610.03695CL2 oct 2026

Language Models that Play Chess and Explain Their Moves

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QUEEN (OURS)2697GEMINI-3.1-PRO2201GPT-5.6-SOL2071GPT-5.6-LUNA182205000 ESTIMATED ELO
fig. estimated eloSmall 4B model outplays frontier LMs

A 4B chess model that plays like a Grandmaster and explains its moves in plain English.

2697Elo

Estimated playing strength after training

Beats every frontier LM tested, near median Grandmaster 2730

How it works

  1. Experts can't explain

    Chess engines play superhumanly but stay silent. Language models explain fluently but play weak moves, so their explanations mislead.

  2. Bridge engine to LM

    Cross-attention links the Lc0 chess encoder to SmolLM3-3B. A quiz curriculum teaches the bridge, then search-based explanations are repeatedly distilled back.

  3. Strong play, solid prose

    Elo rises from 1782 to 2697 over seven rounds. The model tops all baselines on puzzles and matches GPT-5.6-Sol on structural coherence.

FENhidden statestop 3Bellman-styleretrainBoardpositionLc0 chessencoderCross-attentionLMExplainchild movesConsolidateand distillMove plusexplanationFENhidden statestop 3Bellman-styleretrainBoardpositionLc0 chessencoderCross-attentionLMExplainchild movesConsolidateand distillMove plusexplanation

What they found

Which comes out on top on Estimated Elo?

Elo across distillation rounds

try it

Drag the iteration count up and watch playing strength climb.

Distillation iterationsPlaying strengthSeeded, weak playNear GrandmasterQUEEN after seven rounds
Playing strength
medium
here
Seeded, weak play
Each round of consolidating child explanations adds look-ahead, but gains taper off.Illustrative model, not the paper's data

Terms

6 terms

Silent expert A chess engine like Lc0 that plays superbly but outputs no reasons.

Like a student who checks each candidate move with an expert, writes up what happens after each, then merges those notes into one lesson and memorizes it.

Where it breaks
The merged notes can carry invented ideas forward; no expert corrects the prose.

Limits

  • Conceptual coherence scores 2.76, below frontier models; motif hallucinations propagate.
  • Still plays about 290 Elo below its own Leela encoder.
  • Explanation quality judged only by an LM judge, not human players.
From the paper