# LEACE: Perfect linear concept erasure in closed form

arXiv: https://arxiv.org/abs/2306.03819 · HTML: https://mlsanity.com/paper/2306.03819/

## Key facts

- Cited by 267 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 57 references that are in the map.
- First posted on arXiv 6 Jun 2023.

## Builds on (most cited first, 30 of 35)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Bias in Bios: A Case Study of Semantic Representation Bias in a High-Stakes Setting](https://mlsanity.com/paper/1901.09451/) (2019)
- [Universal Dependencies v2: An Evergrowing Multilingual Treebank Collection](https://mlsanity.com/paper/2004.10643/) (2020)
- [Censoring Representations with an Adversary](https://mlsanity.com/paper/1511.05897/) (2015)
- [Adversarial Removal of Demographic Attributes from Text Data](https://mlsanity.com/paper/1808.06640/) (2018)
- [A Theory of Usable Information Under Computational Constraints](https://mlsanity.com/paper/2002.10689/) (2020)
- [All Bark and No Bite: Rogue Dimensions in Transformer Language Models Obscure Representational Quality](https://mlsanity.com/paper/2109.04404/) (2021)
- [Controllable Invariance through Adversarial Feature Learning](https://mlsanity.com/paper/1705.11122/) (2017)
- [Inducing Causal Structure for Interpretable Neural Networks](https://mlsanity.com/paper/2112.00826/) (2021)
- [Interpretability at Scale: Identifying Causal Mechanisms in Alpaca](https://mlsanity.com/paper/2305.08809/) (2023)
- [Linear Adversarial Concept Erasure](https://mlsanity.com/paper/2201.12091/) (2022)
- [Counterfactual Interventions Reveal the Causal Effect of Relative Clause Representations on Agreement Prediction](https://mlsanity.com/paper/2105.06965/) (2021)
- [Adversarial Deep Averaging Networks for Cross-Lingual Sentiment Classification](https://mlsanity.com/paper/1606.01614/) (2016)
- [Kernelized Concept Erasure](https://mlsanity.com/paper/2201.12191/) (2022)
- [Probing Classifiers are Unreliable for Concept Removal and Detection](https://mlsanity.com/paper/2207.04153/) (2022)
- [OSCaR: Orthogonal Subspace Correction and Rectification of Biases in Word Embeddings](https://mlsanity.com/paper/2007.00049/) (2020)
- [The Low-Dimensional Linear Geometry of Contextualized Word Representations](https://mlsanity.com/paper/2105.07109/) (2021)
- [Causal Conceptions of Fairness and their Consequences](https://mlsanity.com/paper/2207.05302/) (2022)
- [Gold Doesn't Always Glitter: Spectral Removal of Linear and Nonlinear Guarded Attribute Information](https://mlsanity.com/paper/2203.07893/) (2022)
- [Can Transformer be Too Compositional? Analysing Idiom Processing in Neural Machine Translation](https://mlsanity.com/paper/2205.15301/) (2022)
- [Efficient fair PCA for fair representation learning](https://mlsanity.com/paper/2302.13319/) (2023)
- [Better Hit the Nail on the Head than Beat around the Bush: Removing Protected Attributes with a Single Projection](https://mlsanity.com/paper/2212.04273/) (2022)

## Built on by (most cited first, 30 of 267)

- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [The WMDP Benchmark: Measuring and Reducing Malicious Use With Unlearning](https://mlsanity.com/paper/2403.03218/) (2024)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [MUSE: Machine Unlearning Six-Way Evaluation for Language Models](https://mlsanity.com/paper/2407.06460/) (2024)
- [Large Language Model Alignment: A Survey](https://mlsanity.com/paper/2309.15025/) (2023)
- [In-Context Unlearning: Language Models as Few Shot Unlearners](https://mlsanity.com/paper/2310.07579/) (2023)
- [An Overview of Catastrophic AI Risks](https://mlsanity.com/paper/2306.12001/) (2023)
- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [Knowledge Editing for Large Language Models: A Survey](https://mlsanity.com/paper/2310.16218/) (2023)
- [Scaling Monosemanticity: Extracting Interpretable Features from Claude 3 Sonnet](https://mlsanity.com/paper/2605.29358/) (2026)
- [A Comprehensive Study of Knowledge Editing for Large Language Models](https://mlsanity.com/paper/2401.01286/) (2024)
- [Improving Instruction-Following in Language Models through Activation Steering](https://mlsanity.com/paper/2410.12877/) (2024)
- [Can Sensitive Information Be Deleted From LLMs? Objectives for Defending Against Extraction Attacks](https://mlsanity.com/paper/2309.17410/) (2023)
- [Tamper-Resistant Safeguards for Open-Weight LLMs](https://mlsanity.com/paper/2408.00761/) (2024)
- [Large Language Model Unlearning via Embedding-Corrupted Prompts](https://mlsanity.com/paper/2406.07933/) (2024)
- [The Geometry of Refusal in Large Language Models: Concept Cones and Representational Independence](https://mlsanity.com/paper/2502.17420/) (2025)
- [AtP*: An efficient and scalable method for localizing LLM behaviour to components](https://mlsanity.com/paper/2403.00745/) (2024)
- [Guardrail Baselines for Unlearning in LLMs](https://mlsanity.com/paper/2403.03329/) (2024)
- [Stay on topic with Classifier-Free Guidance](https://mlsanity.com/paper/2306.17806/) (2023)
- [Detoxifying Large Language Models via Knowledge Editing](https://mlsanity.com/paper/2403.14472/) (2024)
- [Towards Principled Evaluations of Sparse Autoencoders for Interpretability and Control](https://mlsanity.com/paper/2405.08366/) (2024)
- [A Primer on the Inner Workings of Transformer-based Language Models](https://mlsanity.com/paper/2405.00208/) (2024)
- [RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations](https://mlsanity.com/paper/2402.17700/) (2024)
- [RWKU: Benchmarking Real-World Knowledge Unlearning for Large Language Models](https://mlsanity.com/paper/2406.10890/) (2024)
- [Adaptive Activation Steering: A Tuning-Free LLM Truthfulness Improvement Method for Diverse Hallucinations Categories](https://mlsanity.com/paper/2406.00034/) (2024)
- [LLM Unlearning via Loss Adjustment with Only Forget Data](https://mlsanity.com/paper/2410.11143/) (2024)
- [Convergent Linear Representations of Emergent Misalignment](https://mlsanity.com/paper/2506.11618/) (2025)
- [Improving Activation Steering in Language Models with Mean-Centring](https://mlsanity.com/paper/2312.03813/) (2023)

## Abstract (arXiv)

Concept erasure aims to remove specified features from an embedding. It can improve fairness (e.g. preventing a classifier from using gender or race) and interpretability (e.g. removing a concept to observe changes in model behavior). We introduce LEAst-squares Concept Erasure (LEACE), a closed-form method which provably prevents all linear classifiers from detecting a concept while changing the embedding as little as possible, as measured by a broad class of norms. We apply LEACE to large language models with a novel procedure called "concept scrubbing," which erases target concept information from every layer in the network. We demonstrate our method on two tasks: measuring the reliance of language models on part-of-speech information, and reducing gender bias in BERT embeddings. Code is available at https://github.com/EleutherAI/concept-erasure.