# Small Vectors, Big Effects: A Mechanistic Study of RL-Induced Reasoning via Steering Vectors

arXiv: https://arxiv.org/abs/2509.06608 · HTML: https://mlsanity.com/paper/2509.06608/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 24 of its 36 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Mechanistic interpretability / [Steering and interpreting LLM reasoning](https://mlsanity.com/mechinterp/steering-and-interpreting-llm-reasoning/)

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [In-context Vectors: Making In Context Learning More Effective and Controllable Through Latent Space Steering](https://mlsanity.com/paper/2311.06668/) (2023)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [Back to Basics: Revisiting REINFORCE Style Optimization for Learning from Human Feedback in LLMs](https://mlsanity.com/paper/2402.14740/) (2024)
- [Tell me about yourself: LLMs are aware of their learned behaviors](https://mlsanity.com/paper/2501.11120/) (2025)
- [Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn't](https://mlsanity.com/paper/2503.16219/) (2025)
- [Understanding Reasoning in Thinking Language Models via Steering Vectors](https://mlsanity.com/paper/2506.18167/) (2025)
- [Reasoning-Finetuning Repurposes Latent Representations in Base Models](https://mlsanity.com/paper/2507.12638/) (2025)
- [Steering LLM Reasoning Through Bias-Only Adaptation](https://mlsanity.com/paper/2505.18706/) (2025)

## Built on by (most cited first, 8 of 8)

- [From Weights to Activations: Is Steering the Next Frontier of Adaptation?](https://mlsanity.com/paper/2604.14090/) (2026)
- [What Drives Representation Steering? A Mechanistic Case Study on Steering Refusal](https://mlsanity.com/paper/2604.08524/) (2026)
- [Towards a Mechanistic Understanding of Large Reasoning Models: A Survey of Training, Inference, and Failures](https://mlsanity.com/paper/2601.19928/) (2026)
- [KV-Skill: Forging Expertise in the Model's Native Language](https://mlsanity.com/paper/2608.05475/) (2026)
- [Reliable Control-Point Selection for Steering Reasoning in Large Language Models](https://mlsanity.com/paper/2604.02113/) (2026)
- [Mechanistic Interpretability for Neural Networks: Circuits, Sparse Features and Symbolic Reasoning](https://mlsanity.com/paper/2607.07316/) (2026)
- [Sparse Concept Anchoring for Interpretable and Controllable Neural Representations](https://mlsanity.com/paper/2512.12469/) (2025)
- [Activation Flow: Manufacturing Activations for Steering](https://mlsanity.com/paper/2609.32530/) (2026)

## Abstract (arXiv)

The mechanisms by which reasoning training reshapes LLMs' internal computations remain unclear. We study lightweight steering vectors inserted into the base model's residual stream and trained with a reinforcement-learning objective. These vectors explain a large portion of full fine-tuning performance increase while preserving the interpretability of small, additive interventions. We find that (i) the last-layer steering vector acts like a token-substitution bias concentrated on the first generated token, consistently boosting tokens such as "To" and "Step"; (ii) the penultimate-layer vector leaves attention patterns largely intact and instead operates through the MLP and unembedding, preferentially up-weighting process words and structure symbols; and (iii) the steering vectors transfer to other models from the same family. Taken together, these results deepen understanding of how trained steering vectors shape computation and should inform future work in activation engineering and the study of reasoning models.