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

arXiv: https://arxiv.org/abs/2602.19895 · HTML: https://mlsanity.com/paper/2602.19895/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 31)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models](https://mlsanity.com/paper/2201.03544/) (2022)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Right Question is Already Half the Answer: Fully Unsupervised LLM Reasoning Incentivization](https://mlsanity.com/paper/2504.05812/) (2025)
- [The Invisible Leash: Why RLVR May or May Not Escape Its Origin](https://mlsanity.com/paper/2507.14843/) (2025)
- [Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems](https://mlsanity.com/paper/2505.15201/) (2025)
- [Jointly Reinforcing Diversity and Quality in Language Model Generations](https://mlsanity.com/paper/2509.02534/) (2025)
- [T1: Advancing Language Model Reasoning through Reinforcement Learning and Inference Scaling](https://mlsanity.com/paper/2501.11651/) (2025)
- [SRPO: Enhancing Multimodal LLM Reasoning via Reflection-Aware Reinforcement Learning](https://mlsanity.com/paper/2506.01713/) (2025)
- [Diversity-Aware Policy Optimization for Large Language Model Reasoning](https://mlsanity.com/paper/2505.23433/) (2025)
- [On Entropy Control in LLM-RL Algorithms](https://mlsanity.com/paper/2509.03493/) (2025)
- [ETTRL: Balancing Exploration and Exploitation in LLM Test-Time Reinforcement Learning Via Entropy Mechanism](https://mlsanity.com/paper/2508.11356/) (2025)
- [Diversity-Incentivized Exploration for Versatile Reasoning](https://mlsanity.com/paper/2509.26209/) (2025)
- [Progress or Regress? Self-Improvement Reversal in Post-training](https://mlsanity.com/paper/2407.05013/) (2024)
- [Post-training Large Language Models for Diverse High-Quality Responses](https://mlsanity.com/paper/2509.04784/) (2025)
- [Risk-Sensitive RL for Alleviating Exploration Dilemmas in Large Language Models](https://mlsanity.com/paper/2509.24261/) (2025)
- [EEPO: Exploration-Enhanced Policy Optimization via Sample-Then-Forget](https://mlsanity.com/paper/2510.05837/) (2025)

## Built on by (most cited first, 9 of 9)

- [Rebellious Student: Reversing Teacher Signals for Reasoning Exploration with Self-Distilled RLVR](https://mlsanity.com/paper/2605.10781/) (2026)
- [EVE-Agent: Evidence-Verifiable Self-Evolving Agents](https://mlsanity.com/paper/2605.22905/) (2026)
- [Group Entropy-Controlled Policy Optimization](https://mlsanity.com/paper/2607.16850/) (2026)
- [Where Rollouts Begin: Low-Load, High-Leverage First-Token Diversification for RLVR](https://mlsanity.com/paper/2605.28295/) (2026)
- [The Past Is Not Past: Memory-Enhanced Dynamic Reward Shaping](https://mlsanity.com/paper/2604.11297/) (2026)
- [Exploiting Verification-Generation Gap: Test-Time Reinforcement Learning with Confidence-Conditioned Verification](https://mlsanity.com/paper/2606.03608/) (2026)
- [A First-Principles Derivation of LLM Policy Optimization: From Expected Reward to GRPO and Its Structural Extensions](https://mlsanity.com/paper/2606.16733/) (2026)
- [Toward Plasticity-Preserving KL Regularization for Capability Retention in LLM Reinforcement Learning](https://mlsanity.com/paper/2608.01743/) (2026)
- [From Context Shift to Stylistic Collapse: Why Training Objectives Matter More Than Scale](https://mlsanity.com/paper/2605.28826/) (2026)

## Abstract (arXiv)

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.