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Amortized Planning with Large-Scale Transformers: A Case Study on Chess
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Builds ChessBench (10M Lichess games annotated by Stockfish 16) and trains up to 270M-parameter transformers via supervised learning to predict action-values, yielding a searchless chess policy with grandmaster-level Lichess blitz play.
Problem
Whether planning-like search (Stockfish-style value estimation) can be amortized into feed-forward transformers via supervised learning at scale, where memorization is infeasible, and how far such searchless chess policies can go.
Approach
Distill Stockfish 16 action-values (and state-values, oracle best actions) for all legal moves on millions of Lichess boards into decoder-only transformers that predict win-percentage bins with HL-Gauss loss, then play greedily with no search at test time.
Key results
- The 270M transformer reaches a Lichess blitz Elo of 2895 against humans and 2299 tournament Elo, with 95.4% puzzle accuracy on 10K puzzles.
- Action-value prediction outperforms state-value and behavioral cloning in the ablation (83.3% puzzle accuracy vs 77.5% and 65.7%).
- Stockfish 16 at 50ms per move reaches 99.8% puzzle accuracy, and the searchless 270M model nearly matches AlphaZero with 400 MCTS simulations (95.6%).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Scale the model from 9M to 270M parameters | ChessBench action-value Transformer · Internal tournament | Tournament Elo: 2025~($\pm18$) -> 2299~($\pm15$) | Helped |
| Predict state-values instead of action-values (ablation) | 9M Transformer · 1K puzzles (ablation setup) | Puzzle accuracy (%): 83.3 -> 77.5 | Hurt |
| Predict oracle actions instead of action-values (ablation) | 9M Transformer · 1K puzzles (ablation setup) | Puzzle accuracy (%): 83.3 -> 65.7 | Hurt |
| Replace HL-Gauss loss with log loss (ablation) | 9M Transformer · 1K puzzles (ablation setup) | Puzzle accuracy (%): 82.0 -> 80.6 | Hurt |
| Replace HL-Gauss loss with L2 loss (ablation) | 9M Transformer · 1K puzzles (ablation setup) | Puzzle accuracy (%): 82.0 -> 80.8 | Hurt |
| Increase transformer depth from 2 to 16 layers (ablation) | 9M Transformer · 1K puzzles (ablation setup) | Puzzle accuracy (%): 54.7 -> 81.3 | Helped |
| Increase transformer depth from 16 to 32 layers (ablation) | 9M Transformer · 1K puzzles (ablation setup) | Puzzle accuracy (%): 81.3 -> 79.5 | Hurt |
| Use 64 rather than 128 value bins (ablation) | 9M Transformer · 1K puzzles (ablation setup) | Puzzle accuracy (%): 83.8 -> 84.4 | Helped |
| Annotate training data with a 0.1s instead of 0.05s Stockfish limit (ablation) | 9M Transformer · 1K puzzles (ablation setup) | Puzzle accuracy (%): 84.0 -> 85.4 | Helped |
| Use weighted sampling to restore natural board frequencies (ablation) | 9M Transformer · 1K puzzles (ablation setup) | Puzzle accuracy (%): 83.3 -> 49.9 | Hurt |
| Replace the Transformer with an 8-layer residual ConvNet (ablation) | 9M chess policy · 1K puzzles (ablation setup) | Puzzle accuracy (%): 83.3 -> 17.3 | Hurt |
| Increase training data size (ablation) | ChessBench Transformer · 1K puzzles | Puzzle accuracy | Helped |
Surprising findings
- The searchless transformer nearly matches AlphaZero with 400 MCTS simulations on puzzles (95.4% vs 95.6%).
- Behavioral cloning on oracle actions performs much worse than state-value learning even with similar data counts.
Limitations
- The policy does not fully close the gap to Stockfish 16 and perfect distillation remains out of reach.
- Lack of game history causes blindness to threefold repetition and indecisiveness in winning positions.
- Bot-versus-human Elo discrepancy and poor performance on Fischer random chess (1539 Elo) indicate distribution-shift limits.
Experimental setup
Datasets: ChessBench (10M Lichess games annotated with Stockfish 16) Lichess puzzles
Benchmarks: Lichess puzzles (10K) Lichess blitz Elo ChessBench test set
Metrics: puzzle accuracy action accuracy Kendall's tau Elo
Baselines: Stockfish 16 Leela Chess Zero AlphaZero GPT-3.5-turbo-instruct Maia
Builds on: AlphaZero Leela Chess Zero HL-Gauss distributional RL Maia
Closest papers by meaning
- Chess-World-Model: A 10M-Game Benchmark for Exact State Tracking from Chess Move Sequences (NeurIPS 2026 · similarity 0.89)
- Mastering Board Games by External and Internal Planning with Language Models (ICML 2025 · similarity 0.89)
- Implicit Search via Discrete Diffusion: A Study on Chess (ICLR 2025 · similarity 0.88)
- Evidence of Learned Look-Ahead in a Chess-Playing Neural Network (NeurIPS 2024 · similarity 0.88)
- Human-Aligned Chess With a Bit of Search (ICLR 2025 · similarity 0.88)
- The Algorithm Is Not the Behavior: Learned Priors Override Look-Ahead in a Chess-Playing Neural Network (NeurIPS 2026 · similarity 0.88)
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