Let Me Think! A Long Chain of Thought Can Be Worth Exponentially Many Short Ones

Parsa Mirtaheri, Ezra Edelman, Samy Jelassi, Eran Malach, Enric Boix-Adserà

Keywords: reasoning, chain-of-thought, test-time scaling, large language models, transformers, expressivity

TL;DR: demonstrates reasoning settings where scaling the length of chain-of-thought offers an exponential advantage over parallel scaling and aggregation.

Abstract: Inference-time computation has emerged as a promising scaling axis for improving large language model reasoning. However, despite yielding impressive performance, the optimal allocation of inference-time computation remains poorly understood. A central question is whether to prioritize sequential scaling (e.g., longer chains of thought) or parallel scaling (e.g., majority voting across multiple short chains of thought). In this work, we seek to illuminate the landscape of test-time scaling by demonstrating the existence of reasoning settings where sequential scaling offers an exponential advantage over parallel scaling. These settings are based on graph connectivity problems in challenging distributions of graphs. We validate our theoretical findings with comprehensive experiments across a range of language models, including models trained from scratch for graph connectivity with different chain of thought strategies as well as large reasoning models.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 25819