Fractured Chain-of-Thought Reasoning

TL;DR

This paper introduces Fractured Sampling, a novel inference strategy that balances reasoning depth and solution generation to improve the efficiency and accuracy of large language models in reasoning tasks.

Contribution

It proposes Fractured Sampling, a unified approach that interpolates between full Chain-of-Thought and solution-only sampling, optimizing inference efficiency.

Findings

Fractured Sampling outperforms traditional methods in accuracy-cost trade-offs.

It achieves steep log-linear scaling gains in Pass@k versus token budget.

The approach effectively allocates computation for scalable reasoning.

Abstract

Inference-time scaling techniques have significantly bolstered the reasoning capabilities of large language models (LLMs) by harnessing additional computational effort at inference without retraining. Similarly, Chain-of-Thought (CoT) prompting and its extension, Long CoT, improve accuracy by generating rich intermediate reasoning trajectories, but these approaches incur substantial token costs that impede their deployment in latency-sensitive settings. In this work, we first show that truncated CoT, which stops reasoning before completion and directly generates the final answer, often matches full CoT sampling while using dramatically fewer tokens. Building on this insight, we introduce Fractured Sampling, a unified inference-time strategy that interpolates between full CoT and solution-only sampling along three orthogonal axes: (1) the number of reasoning trajectories, (2) the number of final solutions per trajectory, and (3) the depth at which reasoning traces are truncated. Through extensive experiments on five diverse reasoning benchmarks and several model scales, we demonstrate that Fractured Sampling consistently achieves superior accuracy-cost trade-offs, yielding steep log-linear scaling gains in Pass@k versus token budget. Our analysis reveals how to allocate computation across these dimensions to maximize performance, paving the way for more efficient and scalable LLM reasoning. Code is available at https://github.com/BaohaoLiao/frac-cot.