# Out-of-distribution Tests Reveal Compositionality in Chess Transformers

arXiv: https://arxiv.org/abs/2510.20783 · HTML: https://mlsanity.com/paper/2510.20783/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 36 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 22 of 22)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [What Algorithms can Transformers Learn? A Study in Length Generalization](https://mlsanity.com/paper/2310.16028/) (2023)
- [Thinking Like Transformers](https://mlsanity.com/paper/2106.06981/) (2021)
- [Chess as a Testbed for Language Model State Tracking](https://mlsanity.com/paper/2102.13249/) (2021)
- [Amortized Planning with Large-Scale Transformers: A Case Study on Chess](https://mlsanity.com/paper/2402.04494/) (2024)
- [The Chess Transformer: Mastering Play using Generative Language Models](https://mlsanity.com/paper/2008.04057/) (2020)
- [Compositional Capabilities of Autoregressive Transformers: A Study on Synthetic, Interpretable Tasks](https://mlsanity.com/paper/2311.12997/) (2023)
- [On Provable Length and Compositional Generalization](https://mlsanity.com/paper/2402.04875/) (2024)
- [Position: Understanding LLMs Requires More Than Statistical Generalization](https://mlsanity.com/paper/2405.01964/) (2024)
- [Frontier LLMs Still Struggle with Simple Reasoning Tasks](https://mlsanity.com/paper/2507.07313/) (2025)
- [Transcendence: Generative Models Can Outperform The Experts That Train Them](https://mlsanity.com/paper/2406.11741/) (2024)
- [Complete Chess Games Enable LLM Become A Chess Master](https://mlsanity.com/paper/2501.17186/) (2025)
- [Reasoning Beyond Limits: Advances and Open Problems for LLMs](https://mlsanity.com/paper/2503.22732/) (2025)
- [Accelerating Large Language Model Reasoning via Speculative Search](https://mlsanity.com/paper/2505.02865/) (2025)
- [Mastering Chess with a Transformer Model](https://mlsanity.com/paper/2409.12272/) (2024)
- [Towards Understanding the Relationship between In-context Learning and Compositional Generalization](https://mlsanity.com/paper/2403.11834/) (2024)
- [Rule Extrapolation in Language Models: A Study of Compositional Generalization on OOD Prompts](https://mlsanity.com/paper/2409.13728/) (2024)
- [A Taxonomy of Transcendence](https://mlsanity.com/paper/2508.17669/) (2025)
- [Machine Learning Algorithms to Predict Chess960 Result and Develop Opening Themes](https://mlsanity.com/paper/2310.18938/) (2023)

## Built on by (most cited first, 2 of 2)

- [Disentangling generalization and memorization in large language models using chess](https://mlsanity.com/paper/2601.16823/) (2026)
- [How Reasoning Evolves from Post-Training Data: An Empirical Study Using Chess](https://mlsanity.com/paper/2604.05134/) (2026)

## Abstract (arXiv)

Chess is a canonical example of a task that requires rigorous reasoning and long-term planning. Modern decision Transformers - trained similarly to LLMs - are able to learn competent gameplay, but it is unclear to what extent they truly capture the rules of chess. To investigate this, we train a 270M parameter chess Transformer and test it on out-of-distribution scenarios, designed to reveal failures of systematic generalization. Our analysis shows that Transformers exhibit compositional generalization, as evidenced by strong rule extrapolation: they adhere to fundamental syntactic rules of the game by consistently choosing valid moves even in situations very different from the training data. Moreover, they also generate high-quality moves for OOD puzzles. In a more challenging test, we evaluate the models on variants including Chess960 (Fischer Random Chess) - a variant of chess where starting positions of pieces are randomized. We found that while the model exhibits basic strategy adaptation, they are inferior to symbolic AI algorithms that perform explicit search, but gap is smaller when playing against users on Lichess. Moreover, the training dynamics revealed that the model initially learns to move only its own pieces, suggesting an emergent compositional understanding of the game.