# Can LLMs Guide Their Own Exploration? Gradient-Guided Reinforcement Learning for LLM Reasoning

arXiv: https://arxiv.org/abs/2512.15687 · HTML: https://mlsanity.com/paper/2512.15687/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 13 of its 18 references that are in the map.
- First posted on arXiv 17 Dec 2025.

## Placed in

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

## Builds on (most cited first, 13 of 13)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Diversity is All You Need: Learning Skills without a Reward Function](https://mlsanity.com/paper/1802.06070/) (2018)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [Jointly Reinforcing Diversity and Quality in Language Model Generations](https://mlsanity.com/paper/2509.02534/) (2025)
- [Evolving Language Models without Labels: Majority Drives Selection, Novelty Promotes Variation](https://mlsanity.com/paper/2509.15194/) (2025)
- [RESTRAIN: From Spurious Votes to Signals -- Self-Driven RL with Self-Penalization](https://mlsanity.com/paper/2510.02172/) (2025)

## Built on by (most cited first, 10 of 10)

- [GradAlign: Gradient-Aligned Data Selection for LLM Reinforcement Learning](https://mlsanity.com/paper/2602.21492/) (2026)
- [Save the Good Prefix: Precise Error Penalization via Process-Supervised RL to Enhance LLM Reasoning](https://mlsanity.com/paper/2601.18984/) (2026)
- [Why Semantic Entropy Fails: Geometry-Aware and Calibrated Uncertainty for Policy Optimization](https://mlsanity.com/paper/2605.21801/) (2026)
- [Too Correct to Learn: Reinforcement Learning on Saturated Reasoning Data](https://mlsanity.com/paper/2604.18493/) (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)
- [Reasoning or Memorization? Direction-Aware Diversity Exploration in LLM Reinforcement Learning](https://mlsanity.com/paper/2606.10346/) (2026)
- [Instruction-Conditioned Exploration for Reinforcement Learning with Self-Distillation to an Unconditioned Policy](https://mlsanity.com/paper/2608.02087/) (2026)
- [Entropy-Gradient Inversion: Moving Toward Internal Mechanism of Large Reasoning Models](https://mlsanity.com/paper/2605.17770/) (2026)
- [Gradients Know What Outcomes Don't: Unlocking Reinforcement Learning for LLM Reasoning with Gradient-Aligned Rewards](https://mlsanity.com/paper/2609.03342/) (2026)

## Abstract (arXiv)

Reinforcement learning has become essential for strengthening the reasoning abilities of large language models, yet current exploration mechanisms remain fundamentally misaligned with how these models actually learn. Entropy bonuses and external semantic comparators encourage surface level variation but offer no guarantee that sampled trajectories differ in the update directions that shape optimization. We propose G2RL, a gradient guided reinforcement learning framework in which exploration is driven not by external heuristics but by the model own first order update geometry. For each response, G2RL constructs a sequence level feature from the model final layer sensitivity, obtainable at negligible cost from a standard forward pass, and measures how each trajectory would reshape the policy by comparing these features within a sampled group. Trajectories that introduce novel gradient directions receive a bounded multiplicative reward scaler, while redundant or off manifold updates are deemphasized, yielding a self referential exploration signal that is naturally aligned with PPO style stability and KL control. Across math and general reasoning benchmarks (MATH500, AMC, AIME24, AIME25, GPQA, MMLUpro) on Qwen3 base 1.7B and 4B models, G2RL consistently improves pass@1, maj@16, and pass@k over entropy based GRPO and external embedding methods. Analyzing the induced geometry, we find that G2RL expands exploration into substantially more orthogonal and often opposing gradient directions while maintaining semantic coherence, revealing that a policy own update space provides a far more faithful and effective basis for guiding exploration in large language model reinforcement learning.