# Amortized Planning with Large-Scale Transformers: A Case Study on Chess

arXiv: https://arxiv.org/abs/2402.04494 · HTML: https://mlsanity.com/paper/2402.04494/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Mish: A Self Regularized Non-Monotonic Activation Function](https://mlsanity.com/paper/1908.08681/) (2019)
- [Aligning Superhuman AI with Human Behavior: Chess as a Model System](https://mlsanity.com/paper/2006.01855/) (2020)
- [Chess as a Testbed for Language Model State Tracking](https://mlsanity.com/paper/2102.13249/) (2021)
- [Improving Regression Performance with Distributional Losses](https://mlsanity.com/paper/1806.04613/) (2018)
- [The Chess Transformer: Mastering Play using Generative Language Models](https://mlsanity.com/paper/2008.04057/) (2020)
- [Learning Models of Individual Behavior in Chess](https://mlsanity.com/paper/2008.10086/) (2020)
- [DeepChess: End-to-End Deep Neural Network for Automatic Learning in Chess](https://mlsanity.com/paper/1711.09667/) (2017)
- [Giraffe: Using Deep Reinforcement Learning to Play Chess](https://mlsanity.com/paper/1509.01549/) (2015)
- [SentiMATE: Learning to play Chess through Natural Language Processing](https://mlsanity.com/paper/1907.08321/) (2019)
- [Learning Chess With Language Models and Transformers](https://mlsanity.com/paper/2209.11902/) (2022)
- [Move Evaluation in Go Using Deep Convolutional Neural Networks](https://mlsanity.com/paper/1412.6564/) (2014)
- [Learning to Play Chess from Textbooks (LEAP): a Corpus for Evaluating Chess Moves based on Sentiment Analysis](https://mlsanity.com/paper/2310.20260/) (2023)
- [Deep Pepper: Expert Iteration based Chess agent in the Reinforcement Learning Setting](https://mlsanity.com/paper/1806.00683/) (2018)

## Built on by (most cited first, 30 of 49)

- [Stop Regressing: Training Value Functions via Classification for Scalable Deep RL](https://mlsanity.com/paper/2403.03950/) (2024)
- [VideoWorld: Exploring Knowledge Learning from Unlabeled Videos](https://mlsanity.com/paper/2501.09781/) (2025)
- [Causal Language Modeling Can Elicit Search and Reasoning Capabilities on Logic Puzzles](https://mlsanity.com/paper/2409.10502/) (2024)
- [LMAct: A Benchmark for In-Context Imitation Learning with Long Multimodal Demonstrations](https://mlsanity.com/paper/2412.01441/) (2024)
- [Explore the Reasoning Capability of LLMs in the Chess Testbed](https://mlsanity.com/paper/2411.06655/) (2024)
- [Transformers Struggle to Learn to Search](https://mlsanity.com/paper/2412.04703/) (2024)
- [MAPF-GPT: Imitation Learning for Multi-Agent Pathfinding at Scale](https://mlsanity.com/paper/2409.00134/) (2024)
- [LLM CHESS: Benchmarking Reasoning and Instruction-Following in LLMs through Chess](https://mlsanity.com/paper/2512.01992/) (2025)
- [Can Large Language Models Play Games? A Case Study of A Self-Play Approach](https://mlsanity.com/paper/2403.05632/) (2024)
- [Graph-Aware Isomorphic Attention for Adaptive Dynamics in Transformers](https://mlsanity.com/paper/2501.02393/) (2025)
- [Chessformer: A Unified Architecture for Chess Modeling](https://mlsanity.com/paper/2605.19091/) (2026)
- [Lines of Thought in Large Language Models](https://mlsanity.com/paper/2410.01545/) (2024)
- [Advancing Learnable Multi-Agent Pathfinding Solvers with Active Fine-Tuning](https://mlsanity.com/paper/2506.23793/) (2025)
- [Understanding Reasoning from Pretraining to Post-Training](https://mlsanity.com/paper/2607.16097/) (2026)
- [BBA: Bi-Modal Behavioral Alignment for Reasoning with Large Vision-Language Models](https://mlsanity.com/paper/2402.13577/) (2024)
- [Chess Rating Estimation from Moves and Clock Times Using a CNN-LSTM](https://mlsanity.com/paper/2409.11506/) (2024)
- [Learning to Plan via Supervised Contrastive Learning and Strategic Interpolation: A Chess Case Study](https://mlsanity.com/paper/2506.04892/) (2025)
- [ChessArena: A Chess Testbed for Evaluating Strategic Reasoning Capabilities of Large Language Models](https://mlsanity.com/paper/2509.24239/) (2025)
- [Out-of-distribution Tests Reveal Compositionality in Chess Transformers](https://mlsanity.com/paper/2510.20783/) (2025)
- [Exploring Human-AI Conceptual Alignment through the Prism of Chess](https://mlsanity.com/paper/2510.26025/) (2025)
- [Tracing the Thought of a Grandmaster-level Chess-Playing Transformer](https://mlsanity.com/paper/2604.10158/) (2026)
- [Learning Stateful Predictive Knowledge From Experience](https://mlsanity.com/paper/2607.28638/) (2026)
- [Learning the Latent Rules of a Game from Data: A Chess Story](https://mlsanity.com/paper/2410.02426/) (2024)
- [Genomic Next-Token Predictors are In-Context Learners](https://mlsanity.com/paper/2511.12797/) (2025)
- [Disentangling generalization and memorization in large language models using chess](https://mlsanity.com/paper/2601.16823/) (2026)
- [Mixture of Masters: Sparse Chess Language Models with Player Routing](https://mlsanity.com/paper/2602.04447/) (2026)
- [Learning to Communicate Locally for Large-Scale Multi-Agent Pathfinding](https://mlsanity.com/paper/2605.07637/) (2026)
- [GAMBIT: A Three-Mode Benchmark for Adversarial Robustness in Multi-Agent LLM Collectives](https://mlsanity.com/paper/2605.09027/) (2026)
- [A proximal policy optimization based intelligent home solar management](https://mlsanity.com/paper/2404.03888/) (2024)
- [AlphaViT: A flexible game-playing AI for multiple games and variable board sizes](https://mlsanity.com/paper/2408.13871/) (2024)

## Abstract (arXiv)

This paper uses chess, a landmark planning problem in AI, to assess transformers' performance on a planning task where memorization is futile unicodex2013 even at a large scale. To this end, we release ChessBench, a large-scale benchmark dataset of 10 million chess games with legal move and value annotations (15 billion data points) provided by Stockfish 16, the state-of-the-art chess engine. We train transformers with up to 270 million parameters on ChessBench via supervised learning and perform extensive ablations to assess the impact of dataset size, model size, architecture type, and different prediction targets (state-values, action-values, and behavioral cloning). Our largest models learn to predict action-values for novel boards quite accurately, implying highly non-trivial generalization. Despite performing no explicit search, our resulting chess policy solves challenging chess puzzles and achieves a surprisingly strong Lichess blitz Elo of 2895 against humans (grandmaster level). We also compare to Leela Chess Zero and AlphaZero (trained without supervision via self-play) with and without search. We show that, although a remarkably good approximation of Stockfish's search-based algorithm can be distilled into large-scale transformers via supervised learning, perfect distillation is still beyond reach, thus making ChessBench well-suited for future research.