# Activation Steering with a Feedback Controller

arXiv: https://arxiv.org/abs/2510.04309 · HTML: https://mlsanity.com/paper/2510.04309/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 44 of its 64 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)
- LLM safety and security / [Safety alignment, refusal and guardrails](https://mlsanity.com/safety/safety-alignment-refusal-and-guardrails/)
- Mechanistic interpretability / [Activation steering methods](https://mlsanity.com/mechinterp/activation-steering-methods/)

## Builds on (most cited first, 30 of 44)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Microsoft COCO Captions: Data Collection and Evaluation Server](https://mlsanity.com/paper/1504.00325/) (2015)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Quantifying Language Models' Sensitivity to Spurious Features in Prompt Design or: How I learned to start worrying about prompt formatting](https://mlsanity.com/paper/2310.11324/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [Safety Alignment Should Be Made More Than Just a Few Tokens Deep](https://mlsanity.com/paper/2406.05946/) (2024)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [tinyBenchmarks: evaluating LLMs with fewer examples](https://mlsanity.com/paper/2402.14992/) (2024)
- [SDXL-Lightning: Progressive Adversarial Diffusion Distillation](https://mlsanity.com/paper/2402.13929/) (2024)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)

## Built on by (most cited first, 15 of 15)

- [Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control](https://mlsanity.com/paper/2604.19018/) (2026)
- [Activation Steering of Video Generation Models via Reduced-Order Linear Optimal Control](https://mlsanity.com/paper/2606.04775/) (2026)
- [Steering Robustness into World Action Models via Mechanistic Interpretability and Optimal Control](https://mlsanity.com/paper/2607.14943/) (2026)
- [Decomposing how prompting steers behavior](https://mlsanity.com/paper/2606.03093/) (2026)
- [Mechanistic Tomography: Designed Measurement for Control-Oriented Interpretability](https://mlsanity.com/paper/2608.19338/) (2026)
- [ObserverBench: Testing Mechanistic Estimates for Intervention and Control](https://mlsanity.com/paper/2609.03026/) (2026)
- [As Language Models Scale, Low-order Linear Depth Dynamics Emerge](https://mlsanity.com/paper/2603.12541/) (2026)
- [Steer-to-Detect: Probing Hidden Representations for Detection of LLM-Generated Texts](https://mlsanity.com/paper/2605.12890/) (2026)
- [Residual Paving: Diagnosing the Routing Bottleneck in Selective Refusal Editing](https://mlsanity.com/paper/2605.20262/) (2026)
- [AcFlow: Controlling Text-to-Image Diffusion Transformers via Learned Conditional Activation Flow](https://mlsanity.com/paper/2609.10723/) (2026)
- [Replay-Gated Neural Execution: Decoupling Persistent Behavioral Specifications from Neural Realizations in Frozen Language Models](https://mlsanity.com/paper/2609.22243/) (2026)
- [Adaptive Multi-Value Control in LLMs via Causal Activation Steering](https://mlsanity.com/paper/2609.30405/) (2026)
- [One Token Can Be Enough: Bridging Prompting and Activation Steering with Prefix Steering](https://mlsanity.com/paper/2610.04967/) (2026)
- [Noise Out, Bias In: Targeted Bias Injection in Diffusion Language Models via Closed-Loop Activation Steering](https://mlsanity.com/paper/2610.05894/) (2026)
- [Multi-System Cognitive Steering for Generative Communication](https://mlsanity.com/paper/2610.19177/) (2026)

## Abstract (arXiv)

Controlling the behaviors of large language models (LLM) is fundamental to their safety alignment and reliable deployment. However, existing steering methods are primarily driven by empirical insights and lack theoretical performance guarantees. In this work, we develop a control-theoretic foundation for activation steering by showing that popular steering methods correspond to the proportional (P) controllers, with the steering vector serving as the feedback signal. Building on this finding, we propose Proportional-Integral-Derivative (PID) Steering, a principled framework that leverages the full PID controller for activation steering in LLMs. The proportional (P) term aligns activations with target semantic directions, the integral (I) term accumulates errors to enforce persistent corrections across layers, and the derivative (D) term mitigates overshoot by counteracting rapid activation changes. This closed-loop design yields interpretable error dynamics and connects activation steering to classical stability guarantees in control theory. Moreover, PID Steering is lightweight, modular, and readily integrates with state-of-the-art steering methods. Extensive experiments across multiple LLM families and benchmarks demonstrate that PID Steering consistently outperforms existing approaches, achieving more robust and reliable behavioral control. The code is publicly available at: https://github.com/dungnvnus/pid-steering