# A Statistical Physics of Language Model Reasoning

arXiv: https://arxiv.org/abs/2506.04374 · HTML: https://mlsanity.com/paper/2506.04374/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 22 of its 42 references that are in the map.
- First posted on arXiv 4 Jun 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [Towards Understanding Chain-of-Thought Prompting: An Empirical Study of What Matters](https://mlsanity.com/paper/2212.10001/) (2022)
- [CommonsenseQA 2.0: Exposing the Limits of AI through Gamification](https://mlsanity.com/paper/2201.05320/) (2022)
- [Physics of Language Models: Part 1, Learning Hierarchical Language Structures](https://mlsanity.com/paper/2305.13673/) (2023)
- [Linguistic Interpretability of Transformer-based Language Models: a systematic review](https://mlsanity.com/paper/2504.08001/) (2025)

## Built on by (most cited first, 7 of 7)

- [A Survey of Agent Memory in the Second Half: Towards Self-Evolving and Long-Horizon Agents](https://mlsanity.com/paper/2602.06052/) (2026)
- [The wall confronting large language models](https://mlsanity.com/paper/2507.19703/) (2025)
- [Is my model "mind blurting"? Interpreting the dynamics of reasoning tokens with Recurrence Quantification Analysis (RQA)](https://mlsanity.com/paper/2602.06266/) (2026)
- [Semantic Step Prediction: Multi-Step Latent Forecasting in LLM Reasoning Trajectories via Step Sampling](https://mlsanity.com/paper/2604.18464/) (2026)
- [The Geometry of Thought: How Scale Restructures Reasoning In Large Language Models](https://mlsanity.com/paper/2601.13358/) (2026)
- [Phantom Transitions in Language Model Fine-Tuning: A Density-Matrix Analysis](https://mlsanity.com/paper/2606.07559/) (2026)
- [The Depth Flow of Token Representations Is Nonlinear and Does Not Descend Its Own Density](https://mlsanity.com/paper/2608.29706/) (2026)

## Abstract (arXiv)

Transformer LMs show emergent reasoning that resists mechanistic understanding. We offer a statistical physics framework for continuous-time chain-of-thought reasoning dynamics. We model sentence-level hidden state trajectories as a stochastic dynamical system on a lower-dimensional manifold. This drift-diffusion system uses latent regime switching to capture diverse reasoning phases, including misaligned states or failures. Empirical trajectories (8 models, 7 benchmarks) show a rank-40 projection (balancing variance capture and feasibility) explains ~50% variance. We find four latent reasoning regimes. An SLDS model is formulated and validated to capture these features. The framework enables low-cost reasoning simulation, offering tools to study and predict critical transitions like misaligned states or other LM failures.