# Chess as a Testbed for Language Model State Tracking

arXiv: https://arxiv.org/abs/2102.13249 · HTML: https://mlsanity.com/paper/2102.13249/

## Key facts

- Cited by 72 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 26 Feb 2021.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Teaching Machines to Read and Comprehend](https://mlsanity.com/paper/1506.03340/) (2015)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [What do you learn from context? Probing for sentence structure in contextualized word representations](https://mlsanity.com/paper/1905.06316/) (2019)
- [A Corpus and Evaluation Framework for Deeper Understanding of Commonsense Stories](https://mlsanity.com/paper/1604.01696/) (2016)
- [What BERT is not: Lessons from a new suite of psycholinguistic diagnostics for language models](https://mlsanity.com/paper/1907.13528/) (2019)
- [Towards AI-Complete Question Answering: A Set of Prerequisite Toy Tasks](https://mlsanity.com/paper/1502.05698/) (2015)
- [TextWorld: A Learning Environment for Text-based Games](https://mlsanity.com/paper/1806.11532/) (2018)
- [Fine-grained Analysis of Sentence Embeddings Using Auxiliary Prediction Tasks](https://mlsanity.com/paper/1608.04207/) (2016)
- [Information-Theoretic Probing for Linguistic Structure](https://mlsanity.com/paper/2004.03061/) (2020)
- [The Goldilocks Principle: Reading Children's Books with Explicit Memory Representations](https://mlsanity.com/paper/1511.02301/) (2015)
- [Grounded Language Learning in a Simulated 3D World](https://mlsanity.com/paper/1706.06551/) (2017)
- [The Chess Transformer: Mastering Play using Generative Language Models](https://mlsanity.com/paper/2008.04057/) (2020)
- [DeepChess: End-to-End Deep Neural Network for Automatic Learning in Chess](https://mlsanity.com/paper/1711.09667/) (2017)
- [Understanding Early Word Learning in Situated Artificial Agents](https://mlsanity.com/paper/1710.09867/) (2017)

## Built on by (most cited first, 30 of 72)

- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [The Illusion of State in State-Space Models](https://mlsanity.com/paper/2404.08819/) (2024)
- [Fine-Tuning Enhances Existing Mechanisms: A Case Study on Entity Tracking](https://mlsanity.com/paper/2402.14811/) (2024)
- [Evaluating the World Model Implicit in a Generative Model](https://mlsanity.com/paper/2406.03689/) (2024)
- [A Survey on Large Language Model-Based Game Agents](https://mlsanity.com/paper/2404.02039/) (2024)
- [Uncovering mesa-optimization algorithms in Transformers](https://mlsanity.com/paper/2309.05858/) (2023)
- [Large Language Models and Games: A Survey and Roadmap](https://mlsanity.com/paper/2402.18659/) (2024)
- [ChessGPT: Bridging Policy Learning and Language Modeling](https://mlsanity.com/paper/2306.09200/) (2023)
- [Amortized Planning with Large-Scale Transformers: A Case Study on Chess](https://mlsanity.com/paper/2402.04494/) (2024)
- [What Has a Foundation Model Found? Using Inductive Bias to Probe for World Models](https://mlsanity.com/paper/2507.06952/) (2025)
- [Entity Tracking in Language Models](https://mlsanity.com/paper/2305.02363/) (2023)
- [A Language Model's Guide Through Latent Space](https://mlsanity.com/paper/2402.14433/) (2024)
- [Statler: State-Maintaining Language Models for Embodied Reasoning](https://mlsanity.com/paper/2306.17840/) (2023)
- [Evidence of Learned Look-Ahead in a Chess-Playing Neural Network](https://mlsanity.com/paper/2406.00877/) (2024)
- [Learning to Reason and Memorize with Self-Notes](https://mlsanity.com/paper/2305.00833/) (2023)
- [Emergent Representations of Program Semantics in Language Models Trained on Programs](https://mlsanity.com/paper/2305.11169/) (2023)
- [Mixture of Experts Made Intrinsically Interpretable](https://mlsanity.com/paper/2503.07639/) (2025)
- [PhysGame: Uncovering Physical Commonsense Violations in Gameplay Videos](https://mlsanity.com/paper/2412.01800/) (2024)
- [Opening the AI black box: program synthesis via mechanistic interpretability](https://mlsanity.com/paper/2402.05110/) (2024)
- [Transcendence: Generative Models Can Outperform The Experts That Train Them](https://mlsanity.com/paper/2406.11741/) (2024)
- [Finite State Automata Inside Transformers with Chain-of-Thought: A Mechanistic Study on State Tracking](https://mlsanity.com/paper/2502.20129/) (2025)
- [LLM CHESS: Benchmarking Reasoning and Instruction-Following in LLMs through Chess](https://mlsanity.com/paper/2512.01992/) (2025)
- [Improving Chess Commentaries by Combining Language Models with Symbolic Reasoning Engines](https://mlsanity.com/paper/2212.08195/) (2022)
- [Human-aligned Chess with a Bit of Search](https://mlsanity.com/paper/2410.03893/) (2024)
- [ING-VP: MLLMs cannot Play Easy Vision-based Games Yet](https://mlsanity.com/paper/2410.06555/) (2024)
- [Implicit Search via Discrete Diffusion: A Study on Chess](https://mlsanity.com/paper/2502.19805/) (2025)
- [GPT for Games: An Updated Scoping Review (2020-2024)](https://mlsanity.com/paper/2411.00308/) (2024)
- [Large Language Models on the Chessboard: A Study on ChatGPT's Formal Language Comprehension and Complex Reasoning Skills](https://mlsanity.com/paper/2308.15118/) (2023)
- [Representation Matters for Mastering Chess: Improved Feature Representation in AlphaZero Outperforms Switching to Transformers](https://mlsanity.com/paper/2304.14918/) (2023)

## Abstract (arXiv)

Transformer language models have made tremendous strides in natural language understanding tasks. However, the complexity of natural language makes it challenging to ascertain how accurately these models are tracking the world state underlying the text. Motivated by this issue, we consider the task of language modeling for the game of chess. Unlike natural language, chess notations describe a simple, constrained, and deterministic domain. Moreover, we observe that the appropriate choice of chess notation allows for directly probing the world state, without requiring any additional probing-related machinery. We find that: (a) With enough training data, transformer language models can learn to track pieces and predict legal moves with high accuracy when trained solely on move sequences. (b) For small training sets providing access to board state information during training can yield significant improvements. (c) The success of transformer language models is dependent on access to the entire game history i.e. "full attention". Approximating this full attention results in a significant performance drop. We propose this testbed as a benchmark for future work on the development and analysis of transformer language models.