# Interpreting and Controlling LLM Reasoning through Integrated Policy Gradient

arXiv: https://arxiv.org/abs/2602.02313 · HTML: https://mlsanity.com/paper/2602.02313/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 22 of its 53 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 22 of 22)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [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)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Decomposed Prompting: A Modular Approach for Solving Complex Tasks](https://mlsanity.com/paper/2210.02406/) (2022)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Skywork-Reward-V2: Scaling Preference Data Curation via Human-AI Synergy](https://mlsanity.com/paper/2507.01352/) (2025)
- [Compositional Explanations of Neurons](https://mlsanity.com/paper/2006.14032/) (2020)
- [A Comprehensive Survey of Reward Models: Taxonomy, Applications, Challenges, and Future](https://mlsanity.com/paper/2504.12328/) (2025)
- [I Have Covered All the Bases Here: Interpreting Reasoning Features in Large Language Models via Sparse Autoencoders](https://mlsanity.com/paper/2503.18878/) (2025)
- [Unlocking General Long Chain-of-Thought Reasoning Capabilities of Large Language Models via Representation Engineering](https://mlsanity.com/paper/2503.11314/) (2025)
- [A Comprehensive Survey on Trustworthiness in Reasoning with Large Language Models](https://mlsanity.com/paper/2509.03871/) (2025)
- [The Quest for the Right Mediator: Surveying Mechanistic Interpretability Through the Lens of Causal Mediation Analysis](https://mlsanity.com/paper/2408.01416/) (2024)
- [Small Agent Can Also Rock! Empowering Small Language Models as Hallucination Detector](https://mlsanity.com/paper/2406.11277/) (2024)
- [Controllable LLM Reasoning via Sparse Autoencoder-Based Steering](https://mlsanity.com/paper/2601.03595/) (2026)
- [Do Sparse Autoencoders Identify Reasoning Features in Language Models?](https://mlsanity.com/paper/2601.05679/) (2026)
- [KV Cache Steering for Controlling Frozen LLMs](https://mlsanity.com/paper/2507.08799/) (2025)
- [Triggering Chain-of-Thought via Latent Feature Interventions in Large Language Models](https://mlsanity.com/paper/2601.08058/) (2026)

## Built on by (most cited first, 3 of 3)

- [PRISM: A Dual View of LLM Reasoning through Semantic Flow and Latent Computation](https://mlsanity.com/paper/2603.22754/) (2026)
- [LLM Reasoning Is Latent, Not the Chain of Thought](https://mlsanity.com/paper/2604.15726/) (2026)
- [Rep2Skill: Representation-Guided Skill Self-Evolution for LLM Agents](https://mlsanity.com/paper/2609.39149/) (2026)

## Abstract (arXiv)

Large language models (LLMs) demonstrate strong reasoning abilities in solving complex real-world problems. Yet, the internal mechanisms driving these complex reasoning behaviors remain opaque. Existing interpretability approaches targeting reasoning either identify components (e.g., neurons) correlated with special textual patterns, or rely on human-annotated contrastive pairs to derive control vectors. Consequently, current methods struggle to precisely localize complex reasoning mechanisms or capture sequential influence from model internal workings to the reasoning outputs. In this paper, built on outcome-oriented and sequential-influence-aware principles, we focus on identifying components that have sequential contribution to reasoning behavior where outcomes are cumulated by long-range effects. We propose Integrated Policy Gradient (IPG), a novel framework that attributes reasoning behaviors to model's inner components by propagating compound outcome-based signals such as post reasoning accuracy backward through model inference trajectories. Empirical evaluations demonstrate that our approach achieves more precise localization and enables reliable modulation of reasoning behaviors (e.g., reasoning capability, reasoning strength) across diverse reasoning models.