# A Theoretical Understanding of Chain-of-Thought: Coherent Reasoning and Error-Aware Demonstration

arXiv: https://arxiv.org/abs/2410.16540 · HTML: https://mlsanity.com/paper/2410.16540/

## Key facts

- Cited by 13 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 28 of its 32 references that are in the map.
- First posted on arXiv 21 Oct 2024.

## 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, 28 of 28)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Trained Transformers Learn Linear Models In-Context](https://mlsanity.com/paper/2306.09927/) (2023)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [Transformers learn to implement preconditioned gradient descent for in-context learning](https://mlsanity.com/paper/2306.00297/) (2023)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [Towards Understanding Chain-of-Thought Prompting: An Empirical Study of What Matters](https://mlsanity.com/paper/2212.10001/) (2022)
- [The Impact of Reasoning Step Length on Large Language Models](https://mlsanity.com/paper/2401.04925/) (2024)
- [Text and Patterns: For Effective Chain of Thought, It Takes Two to Tango](https://mlsanity.com/paper/2209.07686/) (2022)
- [In-Context Convergence of Transformers](https://mlsanity.com/paper/2310.05249/) (2023)
- [Chain-of-Thought Hub: A Continuous Effort to Measure Large Language Models' Reasoning Performance](https://mlsanity.com/paper/2305.17306/) (2023)
- [Training Dynamics of Multi-Head Softmax Attention for In-Context Learning: Emergence, Convergence, and Optimality](https://mlsanity.com/paper/2402.19442/) (2024)
- [Transformers Implement Functional Gradient Descent to Learn Non-Linear Functions In Context](https://mlsanity.com/paper/2312.06528/) (2023)
- [Analyzing Chain-of-Thought Prompting in Large Language Models via Gradient-based Feature Attributions](https://mlsanity.com/paper/2307.13339/) (2023)
- [Dissecting Chain-of-Thought: Compositionality through In-Context Filtering and Learning](https://mlsanity.com/paper/2305.18869/) (2023)
- [Superiority of Multi-Head Attention in In-Context Linear Regression](https://mlsanity.com/paper/2401.17426/) (2024)
- [Why Can Large Language Models Generate Correct Chain-of-Thoughts?](https://mlsanity.com/paper/2310.13571/) (2023)
- [Theoretical Understanding of In-Context Learning in Shallow Transformers with Unstructured Data](https://mlsanity.com/paper/2402.00743/) (2024)

## Built on by (most cited first, 13 of 13)

- [When More is Less: Understanding Chain-of-Thought Length in LLMs](https://mlsanity.com/paper/2502.07266/) (2025)
- [Audio-Reasoner: Improving Reasoning Capability in Large Audio Language Models](https://mlsanity.com/paper/2503.02318/) (2025)
- [Beyond Examples: High-level Automated Reasoning Paradigm in In-Context Learning via MCTS](https://mlsanity.com/paper/2411.18478/) (2024)
- [Knowing Before Saying: LLM Representations Encode Information About Chain-of-Thought Success Before Completion](https://mlsanity.com/paper/2505.24362/) (2025)
- [Reasoning Beyond Limits: Advances and Open Problems for LLMs](https://mlsanity.com/paper/2503.22732/) (2025)
- [GateLens: A Reasoning-Enhanced LLM Agent for Automotive Software Release Analytics](https://mlsanity.com/paper/2503.21735/) (2025)
- [Reasoning Can Hurt the Inductive Abilities of Large Language Models](https://mlsanity.com/paper/2505.24225/) (2025)
- [FACT-E: Causality-Inspired Evaluation for Trustworthy Chain-of-Thought Reasoning](https://mlsanity.com/paper/2604.10693/) (2026)
- [Bounds of Chain-of-Thought Robustness: Reasoning Steps, Embed Norms, and Beyond](https://mlsanity.com/paper/2509.21284/) (2025)
- [Team Anotheroption at SemEval-2025 Task 8: Bridging the Gap Between Open-Source and Proprietary LLMs in Table QA](https://mlsanity.com/paper/2506.09657/) (2025)
- [A Multimodal Social Agent](https://mlsanity.com/paper/2501.06189/) (2024)
- [Conversational Orientation Reasoning: Egocentric-to-Allocentric Navigation with Multimodal Chain-of-Thought](https://mlsanity.com/paper/2509.18200/) (2025)
- [Demonstrations, CoT, and Prompting: A Theoretical Analysis of ICL](https://mlsanity.com/paper/2603.19611/) (2026)

## Abstract (arXiv)

Few-shot Chain-of-Thought (CoT) prompting has demonstrated strong performance in improving the reasoning capabilities of large language models (LLMs). While theoretical investigations have been conducted to understand CoT, the underlying transformer used in these studies isolates the CoT reasoning process into separated in-context learning steps (Stepwise ICL). In this work, we theoretically show that, compared to Stepwise ICL, the transformer gains better error correction ability and more accurate predictions if the reasoning from earlier steps (Coherent CoT) is integrated. Given that this coherent reasoning changes the behavior of the transformer, we further investigate the sensitivity of the transformer with Coherent CoT when the demonstration examples are corrupted at the inference stage. Our theoretical results indicate that the transformer is more sensitive to errors in intermediate reasoning steps than the final outcome. Building upon this observation, we propose an improvement on CoT by incorporating both correct and incorrect reasoning paths in the demonstration. Our experiments validate the effectiveness of the proposed approach.