# Why think step by step? Reasoning emerges from the locality of experience

arXiv: https://arxiv.org/abs/2304.03843 · HTML: https://mlsanity.com/paper/2304.03843/

## Key facts

- Cited by 103 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 28 references that are in the map.
- First posted on arXiv 7 Apr 2023.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 16 of 16)

- [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)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Data Distributional Properties Drive Emergent In-Context Learning in Transformers](https://mlsanity.com/paper/2205.05055/) (2022)
- [Can language models learn from explanations in context?](https://mlsanity.com/paper/2204.02329/) (2022)
- [Language Model Cascades](https://mlsanity.com/paper/2207.10342/) (2022)

## Built on by (most cited first, 30 of 103)

- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [Chain-of-Thought Reasoning Without Prompting](https://mlsanity.com/paper/2402.10200/) (2024)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [Do Large Language Models Latently Perform Multi-Hop Reasoning?](https://mlsanity.com/paper/2402.16837/) (2024)
- [Benchmark Data Contamination of Large Language Models: A Survey](https://mlsanity.com/paper/2406.04244/) (2024)
- [Skill-it! A Data-Driven Skills Framework for Understanding and Training Language Models](https://mlsanity.com/paper/2307.14430/) (2023)
- [Mind Your Step (by Step): Chain-of-Thought can Reduce Performance on Tasks where Thinking Makes Humans Worse](https://mlsanity.com/paper/2410.21333/) (2024)
- [Position: Graph Foundation Models are Already Here](https://mlsanity.com/paper/2402.02216/) (2024)
- [Generalization v.s. Memorization: Tracing Language Models' Capabilities Back to Pretraining Data](https://mlsanity.com/paper/2407.14985/) (2024)
- [Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization](https://mlsanity.com/paper/2405.15071/) (2024)
- [Igniting Language Intelligence: The Hitchhiker's Guide From Chain-of-Thought Reasoning to Language Agents](https://mlsanity.com/paper/2311.11797/) (2023)
- [Boosting Theory-of-Mind Performance in Large Language Models via Prompting](https://mlsanity.com/paper/2304.11490/) (2023)
- [Towards Better Chain-of-Thought Prompting Strategies: A Survey](https://mlsanity.com/paper/2310.04959/) (2023)
- [Unlocking the Capabilities of Thought: A Reasoning Boundary Framework to Quantify and Optimize Chain-of-Thought](https://mlsanity.com/paper/2410.05695/) (2024)
- [How to think step-by-step: A mechanistic understanding of chain-of-thought reasoning](https://mlsanity.com/paper/2402.18312/) (2024)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [ICLR: In-Context Learning of Representations](https://mlsanity.com/paper/2501.00070/) (2024)
- [Towards autonomous system: flexible modular production system enhanced with large language model agents](https://mlsanity.com/paper/2304.14721/) (2023)
- [From Sparse Dependence to Sparse Attention: Unveiling How Chain-of-Thought Enhances Transformer Sample Efficiency](https://mlsanity.com/paper/2410.05459/) (2024)
- [How do Large Language Models Navigate Conflicts between Honesty and Helpfulness?](https://mlsanity.com/paper/2402.07282/) (2024)
- [Autoregressive Action Sequence Learning for Robotic Manipulation](https://mlsanity.com/paper/2410.03132/) (2024)
- [Fundamental Problems With Model Editing: How Should Rational Belief Revision Work in LLMs?](https://mlsanity.com/paper/2406.19354/) (2024)
- [Do Vision-Language Models Have Internal World Models? Towards an Atomic Evaluation](https://mlsanity.com/paper/2506.21876/) (2025)
- [Understanding Reasoning Ability of Language Models From the Perspective of Reasoning Paths Aggregation](https://mlsanity.com/paper/2402.03268/) (2024)
- [Passive learning of active causal strategies in agents and language models](https://mlsanity.com/paper/2305.16183/) (2023)
- [LLM-Generated Black-box Explanations Can Be Adversarially Helpful](https://mlsanity.com/paper/2405.06800/) (2024)
- [Chain-of-Thought Prompting Obscures Hallucination Cues in Large Language Models: An Empirical Evaluation](https://mlsanity.com/paper/2506.17088/) (2025)
- [Rational Metareasoning for Large Language Models](https://mlsanity.com/paper/2410.05563/) (2024)
- [Learning When to Plan: Efficiently Allocating Test-Time Compute for LLM Agents](https://mlsanity.com/paper/2509.03581/) (2025)
- [Early Stopping Chain-of-thoughts in Large Language Models](https://mlsanity.com/paper/2509.14004/) (2025)

## Abstract (arXiv)

Humans have a powerful and mysterious capacity to reason. Working through a set of mental steps enables us to make inferences we would not be capable of making directly even though we get no additional data from the world. Similarly, when large language models generate intermediate steps (a chain of thought) before answering a question, they often produce better answers than they would directly. We investigate why and how chain-of-thought reasoning is useful in language models, testing the hypothesis that reasoning is effective when training data consists of overlapping local clusters of variables that influence each other strongly. These training conditions enable the chaining of accurate local inferences to estimate relationships between variables that were not seen together in training. We prove that there will exist a "reasoning gap", where reasoning through intermediate variables reduces bias, for the simple case of an autoregressive density estimator trained on local samples from a chain-structured probabilistic model. We then test our hypothesis experimentally in more complex models, training an autoregressive language model on samples from Bayes nets but only including a subset of variables in each sample. We test language models' ability to match conditional probabilities with and without intermediate reasoning steps, finding that intermediate steps are only helpful when the training data is locally structured with respect to dependencies between variables. The combination of locally structured observations and reasoning is much more data-efficient than training on all variables. Our results illustrate how the effectiveness of reasoning step by step is rooted in the local statistical structure of the training data.