Sample Complexity and Representation Ability of Test-time Scaling Paradigms

This paper explores theoretical foundations** for **test-time scaling paradigms** in large language models (LLMs). It **analyzes the sample efficiency** of repeated sampling methods like **self-consistency**, finding it requires more samples (Θ(1/∆²)) than **best-of-n** (Θ(1/∆)) for reliable answers. Furthermore, the paper **investigates the expressive power of self-correction**, demonstrating that Transformers with verifier feedback can simulate online learning, enabling a **single Transformer architecture to solve multiple tasks** without prior task knowledge. The authors **empirically validate their theoretical findings**, showing that self-correction significantly enhances accuracy, especially in larger models.