Training LLMs for Divide-and-Conquer Reasoning Elevates Test-Time Scalability

TL;DR

This paper introduces an end-to-end reinforcement learning framework to improve divide-and-conquer reasoning in large language models, significantly enhancing their test-time scalability and performance on complex tasks.

Contribution

It proposes a novel RL-based training method that aligns DAC reasoning with model capabilities, surpassing chain-of-thought methods in scalability and accuracy.

Findings

DAC framework improves Pass@1 by 8.6%

Enhances test-time scalability of LLMs

Outperforms chain-of-thought reasoning on benchmarks

Abstract

Large language models (LLMs) have demonstrated strong reasoning capabilities through step-by-step chain-of-thought (CoT) reasoning. Nevertheless, at the limits of model capability, CoT often proves insufficient, and its strictly sequential nature constrains test-time scalability. A potential alternative is divide-and-conquer (DAC) reasoning, which decomposes a complex problem into subproblems to facilitate more effective exploration of the solution. Although promising, our analysis reveals a fundamental misalignment between general-purpose post-training and DAC-style inference, which limits the model's capacity to fully leverage this potential. To bridge this gap and fully unlock LLMs' reasoning capabilities on the most challenging tasks, we propose an end-to-end reinforcement learning (RL) framework to enhance their DAC-style reasoning capacity. At each step, the policy decomposes a problem into a group of subproblems, solves them sequentially, and addresses the original one conditioned on the subproblem solutions, with both decomposition and solution integrated into RL training. Under comparable training, our DAC-style framework endows the model with a higher performance ceiling and stronger test-time scalability, surpassing CoT by 8.6% in Pass@1 and 6.3% in Pass@32 on competition-level benchmarks.