# Navigate the Unknown: Enhancing LLM Reasoning with Intrinsic Motivation Guided Exploration

arXiv: https://arxiv.org/abs/2505.17621 · HTML: https://mlsanity.com/paper/2505.17621/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 37 of its 52 references that are in the map.
- First posted on arXiv 23 May 2025.

## Placed in

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

## Builds on (most cited first, 30 of 37)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [A Brief Survey of Deep Reinforcement Learning](https://mlsanity.com/paper/1708.05866/) (2017)
- [Recent Advances in Natural Language Processing via Large Pre-Trained Language Models: A Survey](https://mlsanity.com/paper/2111.01243/) (2021)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [A Systematic Survey of Prompt Engineering in Large Language Models: Techniques and Applications](https://mlsanity.com/paper/2402.07927/) (2024)
- [Count-Based Exploration with Neural Density Models](https://mlsanity.com/paper/1703.01310/) (2017)
- [Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning](https://mlsanity.com/paper/2405.00451/) (2024)
- [Self-Evaluation Guided Beam Search for Reasoning](https://mlsanity.com/paper/2305.00633/) (2023)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [Exploration in Deep Reinforcement Learning: A Survey](https://mlsanity.com/paper/2205.00824/) (2022)
- [Arithmetic Control of LLMs for Diverse User Preferences: Directional Preference Alignment with Multi-Objective Rewards](https://mlsanity.com/paper/2402.18571/) (2024)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [Execution-based Code Generation using Deep Reinforcement Learning](https://mlsanity.com/paper/2301.13816/) (2023)
- [On Designing Effective RL Reward at Training Time for LLM Reasoning](https://mlsanity.com/paper/2410.15115/) (2024)

## Built on by (most cited first, 30 of 34)

- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [SRFT: A Single-Stage Method with Supervised and Reinforcement Fine-Tuning for Reasoning](https://mlsanity.com/paper/2506.19767/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [POPE: Learning to Reason on Hard Problems via Privileged On-Policy Exploration](https://mlsanity.com/paper/2601.18779/) (2026)
- [Skill1: Unified Evolution of Skill-Augmented Agents via Reinforcement Learning](https://mlsanity.com/paper/2605.06130/) (2026)
- [CDE: Curiosity-Driven Exploration for Efficient Reinforcement Learning in Large Language Models](https://mlsanity.com/paper/2509.09675/) (2025)
- [RetroAgent: From Solving to Evolving via Retrospective Dual Intrinsic Feedback](https://mlsanity.com/paper/2603.08561/) (2026)
- [Representation-Based Exploration for Language Models: From Test-Time to Post-Training](https://mlsanity.com/paper/2510.11686/) (2025)
- [Reuse your FLOPs: Scaling RL on Hard Problems by Conditioning on Very Off-Policy Prefixes](https://mlsanity.com/paper/2601.18795/) (2026)
- [Risk-Sensitive RL for Alleviating Exploration Dilemmas in Large Language Models](https://mlsanity.com/paper/2509.24261/) (2025)
- [Clip-Low Increases Entropy and Clip-High Decreases Entropy in Reinforcement Learning of Large Language Models](https://mlsanity.com/paper/2509.26114/) (2025)
- [Don't Waste Mistakes: Leveraging Negative RL-Groups via Confidence Reweighting](https://mlsanity.com/paper/2510.08696/) (2025)
- [Revisiting Entropy Regularization: Adaptive Coefficient Unlocks Its Potential for LLM Reinforcement Learning](https://mlsanity.com/paper/2510.10959/) (2025)
- [Count Counts: Motivating Exploration in LLM Reasoning with Count-based Intrinsic Rewards](https://mlsanity.com/paper/2510.16614/) (2025)
- [Expanding LLM Agent Boundaries with Strategy-Guided Exploration](https://mlsanity.com/paper/2603.02045/) (2026)
- [Dual-Uncertainty Guided Policy Learning for Multimodal Reasoning](https://mlsanity.com/paper/2510.01444/) (2025)
- [MemSearch-o1: Empowering Large Language Models with Reasoning-Aligned Memory Growth in Agentic Search](https://mlsanity.com/paper/2604.17265/) (2026)
- [Poly-EPO: Training Exploratory Reasoning Models](https://mlsanity.com/paper/2604.17654/) (2026)
- [BaNEL: Exploration Posteriors for Generative Modeling Using Only Negative Rewards](https://mlsanity.com/paper/2510.09596/) (2025)
- [Beyond Alignment: Expanding Reasoning Capacity via Manifold-Reshaping Policy Optimization](https://mlsanity.com/paper/2602.02545/) (2026)
- [From Curiosity to Caution: Mitigating Reward Hacking for Best-of-N with Pessimism](https://mlsanity.com/paper/2604.04648/) (2026)
- [Tandem: Riding Together with Large and Small Language Models for Efficient Reasoning](https://mlsanity.com/paper/2604.23623/) (2026)
- [How You Begin is How You Reason: Driving Exploration in RLVR via Prefix-Tuned Priors](https://mlsanity.com/paper/2605.08817/) (2026)
- [On Advantage Estimates for Max@K Policy Gradients](https://mlsanity.com/paper/2606.06080/) (2026)
- [OrderGrad: Optimizing Beyond the Mean with Order-Statistic Policy Gradient Estimation](https://mlsanity.com/paper/2606.06096/) (2026)
- [Modularized Reinforcement Learning on LLMs: From MDP Creation to Exploration and Learning](https://mlsanity.com/paper/2606.21943/) (2026)
- [Why Did Apple Fall: Evaluating Curiosity in Large Language Models](https://mlsanity.com/paper/2510.20635/) (2025)
- [BRIDGE: Bridging Reasoning In Distillation Gap Elimination via Structure-Aware Masking](https://mlsanity.com/paper/2602.17686/) (2026)
- [AdapTime: Enabling Adaptive Temporal Reasoning in Large Language Models](https://mlsanity.com/paper/2604.24175/) (2026)
- [MultiDx: A Multi-Source Knowledge Integration Framework towards Diagnostic Reasoning](https://mlsanity.com/paper/2604.24186/) (2026)

## Abstract (arXiv)

Reinforcement Learning (RL) has become a key approach for enhancing the reasoning capabilities of large language models. However, prevalent RL approaches like proximal policy optimization and group relative policy optimization suffer from sparse, outcome-based rewards and weak exploration incentives, limiting their effectiveness. Specifically, sparse rewards offer limited feedback, especially on difficult problems, and introduce biases favoring familiar trajectories over novel reasoning paths. These issues critically undermine performance on complex tasks that inherently require iterative reasoning. To overcome these challenges, we propose Intrinsic MotivAtion Guided exploratIoN for Enhanced reasoning (IMAGINE), which delivers dense rewards and encourages exploration. IMAGINE introduces three innovations: a trajectory-aware exploration reward that reduces token-level bias efficiently; an error-conditioned reward allocation that promotes efficient exploration on hard samples while stabilizing training; and an advantage-preserving integration mechanism that retains distributional integrity during learning. Experiments on four public datasets show that IMAGINE improves performance by 22.23% on AIME 2024.