Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought

This research paper explores how Chain of Thought (CoT) prompting enables transformers to solve complex mathematical problems by mimicking iterative optimization techniques. The authors demonstrate that while standard models are limited to a single stage of calculation, using intermediate reasoning steps allows a transformer to execute multi-step gradient descent internally. Through the lens of linear regression tasks, the study proves that this autoregressive process leads to a near-perfect recovery of underlying data patterns that simpler models cannot capture. Furthermore, the findings indicate that looped architectures and CoT significantly boost the ability of these models to generalize to new information. Ultimately, the work provides a formal theoretical framework to explain why breaking down problems into smaller parts enhances the algorithmic power of large language models.