# Representation Surgery: Theory and Practice of Affine Steering

arXiv: https://arxiv.org/abs/2402.09631 · HTML: https://mlsanity.com/paper/2402.09631/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 43 references that are in the map.
- First posted on arXiv 15 Feb 2024.

## Builds on (most cited first, 28 of 28)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [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)
- [Universal Adversarial Triggers for Attacking and Analyzing NLP](https://mlsanity.com/paper/1908.07125/) (2019)
- [The Woman Worked as a Babysitter: On Biases in Language Generation](https://mlsanity.com/paper/1909.01326/) (2019)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [DExperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts](https://mlsanity.com/paper/2105.03023/) (2021)
- [Bias in Bios: A Case Study of Semantic Representation Bias in a High-Stakes Setting](https://mlsanity.com/paper/1901.09451/) (2019)
- [Lipstick on a Pig: Debiasing Methods Cover up Systematic Gender Biases in Word Embeddings But do not Remove Them](https://mlsanity.com/paper/1903.03862/) (2019)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [Extracting Latent Steering Vectors from Pretrained Language Models](https://mlsanity.com/paper/2205.05124/) (2022)
- [Demographic Dialectal Variation in Social Media: A Case Study of African-American English](https://mlsanity.com/paper/1608.08868/) (2016)
- [Adversarial Removal of Demographic Attributes from Text Data](https://mlsanity.com/paper/1808.06640/) (2018)
- [Learning Gender-Neutral Word Embeddings](https://mlsanity.com/paper/1809.01496/) (2018)
- [CausaLM: Causal Model Explanation Through Counterfactual Language Models](https://mlsanity.com/paper/2005.13407/) (2020)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [Kernelized Concept Erasure](https://mlsanity.com/paper/2201.12191/) (2022)
- [Unified Detoxifying and Debiasing in Language Generation via Inference-time Adaptive Optimization](https://mlsanity.com/paper/2210.04492/) (2022)
- [A Geometric Notion of Causal Probing](https://mlsanity.com/paper/2307.15054/) (2023)
- [Goodtriever: Adaptive Toxicity Mitigation with Retrieval-augmented Models](https://mlsanity.com/paper/2310.07589/) (2023)
- [Domain-Adaptive Pretraining Methods for Dialogue Understanding](https://mlsanity.com/paper/2105.13665/) (2021)

## Built on by (most cited first, 30 of 50)

- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [A Primer on the Inner Workings of Transformer-based Language Models](https://mlsanity.com/paper/2405.00208/) (2024)
- [Spectral Editing of Activations for Large Language Model Alignment](https://mlsanity.com/paper/2405.09719/) (2024)
- [Angular Steering: Behavior Control via Rotation in Activation Space](https://mlsanity.com/paper/2510.26243/) (2025)
- [LLaVA Steering: Visual Instruction Tuning with 500x Fewer Parameters through Modality Linear Representation-Steering](https://mlsanity.com/paper/2412.12359/) (2024)
- [Understanding (Un)Reliability of Steering Vectors in Language Models](https://mlsanity.com/paper/2505.22637/) (2025)
- [A Unified Understanding and Evaluation of Steering Methods](https://mlsanity.com/paper/2502.02716/) (2025)
- [The Quest for the Right Mediator: Surveying Mechanistic Interpretability Through the Lens of Causal Mediation Analysis](https://mlsanity.com/paper/2408.01416/) (2024)
- [Controllable Context Sensitivity and the Knob Behind It](https://mlsanity.com/paper/2411.07404/) (2024)
- [ODESteer: A Unified ODE-Based Steering Framework for LLM Alignment](https://mlsanity.com/paper/2602.17560/) (2026)
- [Gumbel Counterfactual Generation From Language Models](https://mlsanity.com/paper/2411.07180/) (2024)
- [SAKE: Steering Activations for Knowledge Editing](https://mlsanity.com/paper/2503.01751/) (2025)
- [Emergence of Linear Truth Encodings in Language Models](https://mlsanity.com/paper/2510.15804/) (2025)
- [From Directions to Regions: Decomposing Activations in Language Models via Local Geometry](https://mlsanity.com/paper/2602.02464/) (2026)
- [Can LLMs Introspect? A Reality Check](https://mlsanity.com/paper/2605.26242/) (2026)
- [The Information Geometry of Softmax: Probing and Steering](https://mlsanity.com/paper/2602.15293/) (2026)
- [Curveball Steering: The Right Direction To Steer Isn't Always Linear](https://mlsanity.com/paper/2603.09313/) (2026)
- [Interpretation Meets Safety: A Survey on Interpretation Methods and Tools for Improving LLM Safety](https://mlsanity.com/paper/2506.05451/) (2025)
- [Mitigating Hallucination in VideoLLMs via Temporal-Aware Activation Engineering](https://mlsanity.com/paper/2505.12826/) (2025)
- [ReCoVeR the Target Language: Language Steering without Sacrificing Task Performance](https://mlsanity.com/paper/2509.14814/) (2025)
- [Concept Heterogeneity-aware Representation Steering](https://mlsanity.com/paper/2603.02237/) (2026)
- [FishBack: Pullback Fisher Geometry for Optimal Activation Steering in Transformers](https://mlsanity.com/paper/2605.17231/) (2026)
- [DISCO: Disentangled Communication Steering for Large Language Models](https://mlsanity.com/paper/2509.16820/) (2025)
- [Toward a Flexible Framework for Linear Representation Hypothesis Using Maximum Likelihood Estimation](https://mlsanity.com/paper/2502.16385/) (2025)
- [Nonlinear Concept Erasure: a Density Matching Approach](https://mlsanity.com/paper/2507.12341/) (2025)
- [Redefining Experts: Interpretable Decomposition of Language Models for Toxicity Mitigation](https://mlsanity.com/paper/2509.16660/) (2025)
- [Where to Steer: Input-Dependent Layer Selection for Steering Improves LLM Alignment](https://mlsanity.com/paper/2604.03867/) (2026)
- [Conceptors for Semantic Steering](https://mlsanity.com/paper/2605.04980/) (2026)
- [Don't Lose Focus: Activation Steering via Key-Orthogonal Projections](https://mlsanity.com/paper/2605.06342/) (2026)
- [Distributional Surgery for Language Model Activations](https://mlsanity.com/paper/2501.15758/) (2025)

## Abstract (arXiv)

Language models often exhibit undesirable behavior, e.g., generating toxic or gender-biased text. In the case of neural language models, an encoding of the undesirable behavior is often present in the model's representations. Thus, one natural (and common) approach to prevent the model from exhibiting undesirable behavior is to steer the model's representations in a manner that reduces the probability of it generating undesirable text. This paper investigates the formal and empirical properties of steering functions, i.e., transformation of the neural language model's representations that alter its behavior. First, we derive two optimal, in the least-squares sense, affine steering functions under different constraints. Our theory provides justification for existing approaches and offers a novel, improved steering approach. Second, we offer a series of experiments that demonstrate the empirical effectiveness of the methods in mitigating bias and reducing toxic generation.