DSDR: Dual-Scale Diversity Regularization for Exploration in LLM Reasoning

TL;DR

This paper introduces DSDR, a dual-scale diversity regularization framework for reinforcement learning with verifiers in large language model reasoning, enhancing exploration and accuracy.

Contribution

The paper proposes a novel dual-scale regularization method that decomposes diversity into global and local components, improving exploration in LLM reasoning tasks.

Findings

DSDR improves accuracy and pass@k in reasoning benchmarks.

It maintains diversity among correct reasoning trajectories.

Theoretical analysis supports optimal correctness preservation.

Abstract

Reinforcement learning with verifiers (RLVR) is a central paradigm for improving large language model (LLM) reasoning, yet existing methods often suffer from limited exploration. Policies tend to collapse onto a few reasoning patterns and prematurely stop deep exploration, while conventional entropy regularization introduces only local stochasticity and fails to induce meaningful path-level diversity, leading to weak and unstable learning signals in group-based policy optimization. We propose DSDR, a Dual-Scale Diversity Regularization reinforcement learning framework that decomposes diversity in LLM reasoning into global and coupling components. Globally, DSDR promotes diversity among correct reasoning trajectories to explore distinct solution modes. Locally, it applies a length-invariant, token-level entropy regularization restricted to correct trajectories, preventing entropy collapse within each mode while preserving correctness. The two scales are coupled through a global-to-local allocation mechanism that emphasizes local regularization for more distinctive correct trajectories. We provide theoretical support showing that DSDR preserves optimal correctness under bounded regularization, sustains informative learning signals in group-based optimization, and yields a principled global-to-local coupling rule. Experiments on multiple reasoning benchmarks demonstrate consistent improvements in accuracy and pass@k, highlighting the importance of dual-scale diversity for deep exploration in RLVR. Code is available at https://github.com/SUSTechBruce/DSDR.