# Training Nonlinear Transformers for Chain-of-Thought Inference: A Theoretical Generalization Analysis

arXiv: https://arxiv.org/abs/2410.02167 · HTML: https://mlsanity.com/paper/2410.02167/

## Key facts

- Cited by 14 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 49 of its 56 references that are in the map.
- First posted on arXiv 3 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, 30 of 49)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [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)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [Sora: A Review on Background, Technology, Limitations, and Opportunities of Large Vision Models](https://mlsanity.com/paper/2402.17177/) (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)
- [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)
- [Chain-of-Thought Reasoning Without Prompting](https://mlsanity.com/paper/2402.10200/) (2024)
- [How Transformers Learn Causal Structure with Gradient Descent](https://mlsanity.com/paper/2402.14735/) (2024)
- [In-Context Convergence of Transformers](https://mlsanity.com/paper/2310.05249/) (2023)
- [Can Mamba Learn How to Learn? A Comparative Study on In-Context Learning Tasks](https://mlsanity.com/paper/2402.04248/) (2024)
- [Scan and Snap: Understanding Training Dynamics and Token Composition in 1-layer Transformer](https://mlsanity.com/paper/2305.16380/) (2023)
- [How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?](https://mlsanity.com/paper/2310.08391/) (2023)
- [Vision Transformers provably learn spatial structure](https://mlsanity.com/paper/2210.09221/) (2022)
- [How Do Transformers Learn Topic Structure: Towards a Mechanistic Understanding](https://mlsanity.com/paper/2303.04245/) (2023)
- [A Theoretical Understanding of Shallow Vision Transformers: Learning, Generalization, and Sample Complexity](https://mlsanity.com/paper/2302.06015/) (2023)
- [How Do Transformers Learn In-Context Beyond Simple Functions? A Case Study on Learning with Representations](https://mlsanity.com/paper/2310.10616/) (2023)

## Built on by (most cited first, 14 of 14)

- [Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens](https://mlsanity.com/paper/2508.01191/) (2025)
- [When is Task Vector Provably Effective for Model Editing? A Generalization Analysis of Nonlinear Transformers](https://mlsanity.com/paper/2504.10957/) (2025)
- [How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias](https://mlsanity.com/paper/2505.00926/) (2025)
- [Compositional Generalization from Learned Skills via CoT Training: A Theoretical and Structural Analysis for Reasoning](https://mlsanity.com/paper/2502.04667/) (2025)
- [RL-STaR: Theoretical Analysis of Reinforcement Learning Frameworks for Self-Taught Reasoner](https://mlsanity.com/paper/2410.23912/) (2024)
- [A Theoretical Framework for OOD Robustness in Transformers using Gevrey Classes](https://mlsanity.com/paper/2504.12991/) (2025)
- [Provable Benefit of Curriculum in Transformer Tree-Reasoning Post-Training](https://mlsanity.com/paper/2511.07372/) (2025)
- [Continuous Latent Contexts Enable Efficient Online Learning in Transformers](https://mlsanity.com/paper/2605.09867/) (2026)
- [Dynamics of Spontaneous Topic Changes in Next Token Prediction with Self-Attention](https://mlsanity.com/paper/2501.06382/) (2025)
- [Bounds of Chain-of-Thought Robustness: Reasoning Steps, Embed Norms, and Beyond](https://mlsanity.com/paper/2509.21284/) (2025)
- [How Can Mamba Learn In Context with Outliers and Generalize Provably?](https://mlsanity.com/paper/2510.00399/) (2025)
- [Visual prompting reimagined: The power of the Activation Prompts](https://mlsanity.com/paper/2604.06440/) (2026)
- [Robust Heterogeneous Analog-Digital Computing for Mixture-of-Experts Models with Theoretical Generalization Guarantees](https://mlsanity.com/paper/2603.02633/) (2026)
- [Transformers Learn the Optimal DDPM Denoiser for Multi-Token GMMs](https://mlsanity.com/paper/2604.10074/) (2026)

## Abstract (arXiv)

Chain-of-Thought (CoT) is an efficient prompting method that enables the reasoning ability of large language models by augmenting the query using multiple examples with multiple intermediate steps. Despite the empirical success, the theoretical understanding of how to train a Transformer to achieve the CoT ability remains less explored. This is primarily due to the technical challenges involved in analyzing the nonconvex optimization on nonlinear attention models. To the best of our knowledge, this work provides the first theoretical study of training Transformers with nonlinear attention to obtain the CoT generalization capability so that the resulting model can inference on unseen tasks when the input is augmented by examples of the new task. We first quantify the required training samples and iterations to train a Transformer model towards CoT ability. We then prove the success of its CoT generalization on unseen tasks with distribution-shifted testing data. Moreover, we theoretically characterize the conditions for an accurate reasoning output by CoT even when the provided reasoning examples contain noises and are not always accurate. In contrast, in-context learning (ICL), which can be viewed as one-step CoT without intermediate steps, may fail to provide an accurate output when CoT does. These theoretical findings are justified through experiments.