# Reasoning or Memorization? Direction-Aware Diversity Exploration in LLM Reinforcement Learning

arXiv: https://arxiv.org/abs/2606.10346 · HTML: https://mlsanity.com/paper/2606.10346/

## 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 14 of its 32 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Placed in

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

## Builds on (most cited first, 14 of 14)

- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Language Models are Multilingual Chain-of-Thought Reasoners](https://mlsanity.com/paper/2210.03057/) (2022)
- [Measuring Compositional Generalization: A Comprehensive Method on Realistic Data](https://mlsanity.com/paper/1912.09713/) (2019)
- [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)
- [Can LLMs Guide Their Own Exploration? Gradient-Guided Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2512.15687/) (2025)

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

- [Beyond Fixed Directions: Adaptive Representation Analysis of Reasoning and Memorization in LLMs](https://mlsanity.com/paper/2608.21919/) (2026)
- [FlowBalance: Verifier-Grounded Self-Improvement from On-Policy Reasoning Experience](https://mlsanity.com/paper/2609.03241/) (2026)

## Abstract (arXiv)

Reinforcement learning has become a key paradigm for eliciting reasoning abilities in large language models, where exploration is crucial for discovering effective solution trajectories. Existing exploration methods typically encourage diversity in semantic or gradient spaces, without distinguishing what drives this diversity. A trajectory may appear novel because it follows a new reasoning process, or because it varies memorized patterns and shortcuts. Rewarding both cases equally may steer exploration toward memorization rather than genuine reasoning improvement. In this paper, we propose DiRL, a Direction-Aware Reinforcement Learning framework that anchors exploration to an internal reasoning-memorization direction of the policy. Specifically, DiRL extracts this direction from model representations, constructs direction-weighted gradient features to characterize rollout updates, and shapes rewards to amplify reasoning-aligned exploration while suppressing memorization-aligned variations. DiRL integrates seamlessly into standard Group Relative Policy Optimization (GRPO). Extensive experiments on mathematical and general reasoning benchmarks demonstrate the effectiveness of DiRL, showing significant improvements over various existing exploration methods.