# How You Begin is How You Reason: Driving Exploration in RLVR via Prefix-Tuned Priors

arXiv: https://arxiv.org/abs/2605.08817 · HTML: https://mlsanity.com/paper/2605.08817/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 35 of its 54 references that are in the map.
- First posted on arXiv 9 May 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- End-to-end autonomous driving / [Reasoning VLA and VLM driving policies](https://mlsanity.com/driving/reasoning-vla-and-vlm-driving-policies/)

## Builds on (most cited first, 30 of 35)

- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [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)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [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)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [SFT or RL? An Early Investigation into Training R1-Like Reasoning Large Vision-Language Models](https://mlsanity.com/paper/2504.11468/) (2025)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [LLM Post-Training: A Deep Dive into Reasoning Large Language Models](https://mlsanity.com/paper/2502.21321/) (2025)
- [Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving](https://mlsanity.com/paper/2507.23726/) (2025)
- [The Invisible Leash: Why RLVR May or May Not Escape Its Origin](https://mlsanity.com/paper/2507.14843/) (2025)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [An Empirical Study on Eliciting and Improving R1-like Reasoning Models](https://mlsanity.com/paper/2503.04548/) (2025)
- [First Return, Entropy-Eliciting Explore](https://mlsanity.com/paper/2507.07017/) (2025)
- [Navigate the Unknown: Enhancing LLM Reasoning with Intrinsic Motivation Guided Exploration](https://mlsanity.com/paper/2505.17621/) (2025)
- [Diversity-Incentivized Exploration for Versatile Reasoning](https://mlsanity.com/paper/2509.26209/) (2025)
- [Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward](https://mlsanity.com/paper/2510.03222/) (2025)

## Built on by (most cited first, 2 of 2)

- [The Model Knows Another Way: Strategy Switching for Effective RLVR Exploration](https://mlsanity.com/paper/2609.33085/) (2026)
- [EAPO: Entropy-Driven Adaptive Positive-Negative Sample Weighting for Policy Optimization in Open-Ended QA](https://mlsanity.com/paper/2605.27846/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) recently thrives in large language model (LLM) reasoning tasks. However, the reward sparsity and the long reasoning horizon make effective exploration challenging. In practice, this challenge manifests as the entropy collapse phenomenon, where RLVR improves single-rollout accuracy but fails to expand coverage on successful reasoning trajectories. Passive exploration techniques like entropy regularization tend to dismiss generation quality, resulting in noisy rollouts. In response to this issue, we propose an Information-Maximizing Augmented eXploration (IMAX) framework to train a pool of soft prefixes that reshapes the base model's prior over reasoning trajectories. Rather than relying on RL to incentivize exploration on top of the base model, each prefix acts as a trainable control knob that induces a distinct rollout distribution from the same backbone model. To encourage discovery of diverse and task-relevant reasoning behaviors, we derive an Information Maximization (InfoMax) reward to complement the verifiable rewards for RL training. IMAX is in general algorithm-agnostic and can be seamlessly integrated into existing RLVR pipelines. Experiment results have shown that across three backbone scales, IMAX consistently improves reasoning performance over standard RLVR, with gains up to 11.60% in Pass@4 and 10.57% in Avg@4.