# Linear Adversarial Concept Erasure

arXiv: https://arxiv.org/abs/2201.12091 · HTML: https://mlsanity.com/paper/2201.12091/

## Key facts

- Cited by 101 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 74 references that are in the map.
- First posted on arXiv 28 Jan 2022.

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

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Semantics derived automatically from language corpora contain human-like biases](https://mlsanity.com/paper/1608.07187/) (2016)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [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)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Censoring Representations with an Adversary](https://mlsanity.com/paper/1511.05897/) (2015)
- [SimLex-999: Evaluating Semantic Models with (Genuine) Similarity Estimation](https://mlsanity.com/paper/1408.3456/) (2014)
- [Adversarial Removal of Demographic Attributes from Text Data](https://mlsanity.com/paper/1808.06640/) (2018)
- [Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods](https://mlsanity.com/paper/1902.08297/) (2019)
- [Intrinsic Bias Metrics Do Not Correlate with Application Bias](https://mlsanity.com/paper/2012.15859/) (2020)
- [Controllable Invariance through Adversarial Feature Learning](https://mlsanity.com/paper/1705.11122/) (2017)
- [Debiasing Pre-trained Contextualised Embeddings](https://mlsanity.com/paper/2101.09523/) (2021)
- [The Complexity of Constrained Min-Max Optimization](https://mlsanity.com/paper/2009.09623/) (2020)
- [Accelerated Algorithms for Smooth Convex-Concave Minimax Problems with O(1/k2) Rate on Squared Gradient Norm](https://mlsanity.com/paper/2102.07922/) (2021)
- [Attenuating Bias in Word Vectors](https://mlsanity.com/paper/1901.07656/) (2019)
- [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)
- [From Facial Parts Responses to Face Detection: A Deep Learning Approach](https://mlsanity.com/paper/1509.06451/) (2015)
- [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)
- [Improved Algorithms for Convex-Concave Minimax Optimization](https://mlsanity.com/paper/2006.06359/) (2020)

## Built on by (most cited first, 30 of 101)

- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)
- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [Toward Transparent AI: A Survey on Interpreting the Inner Structures of Deep Neural Networks](https://mlsanity.com/paper/2207.13243/) (2022)
- [A Survey on Fairness in Large Language Models](https://mlsanity.com/paper/2308.10149/) (2023)
- [A Primer on the Inner Workings of Transformer-based Language Models](https://mlsanity.com/paper/2405.00208/) (2024)
- [Probing for the Usage of Grammatical Number](https://mlsanity.com/paper/2204.08831/) (2022)
- [Self-Destructing Models: Increasing the Costs of Harmful Dual Uses of Foundation Models](https://mlsanity.com/paper/2211.14946/) (2022)
- [Probing Classifiers are Unreliable for Concept Removal and Detection](https://mlsanity.com/paper/2207.04153/) (2022)
- [Steering Out-of-Distribution Generalization with Concept Ablation Fine-Tuning](https://mlsanity.com/paper/2507.16795/) (2025)
- [Gender Artifacts in Visual Datasets](https://mlsanity.com/paper/2206.09191/) (2022)
- [Machine Unlearning Fails to Remove Data Poisoning Attacks](https://mlsanity.com/paper/2406.17216/) (2024)
- [Immunization against harmful fine-tuning attacks](https://mlsanity.com/paper/2402.16382/) (2024)
- [Gold Doesn't Always Glitter: Spectral Removal of Linear and Nonlinear Guarded Attribute Information](https://mlsanity.com/paper/2203.07893/) (2022)
- [MABEL: Attenuating Gender Bias using Textual Entailment Data](https://mlsanity.com/paper/2210.14975/) (2022)
- [Parameter-efficient Modularised Bias Mitigation via AdapterFusion](https://mlsanity.com/paper/2302.06321/) (2023)
- [Shielded Representations: Protecting Sensitive Attributes Through Iterative Gradient-Based Projection](https://mlsanity.com/paper/2305.10204/) (2023)
- [A Geometric Notion of Causal Probing](https://mlsanity.com/paper/2307.15054/) (2023)
- [Debiasing Algorithm through Model Adaptation](https://mlsanity.com/paper/2310.18913/) (2023)
- [Efficient fair PCA for fair representation learning](https://mlsanity.com/paper/2302.13319/) (2023)
- [Controllable Context Sensitivity and the Knob Behind It](https://mlsanity.com/paper/2411.07404/) (2024)
- [BLIND: Bias Removal With No Demographics](https://mlsanity.com/paper/2212.10563/) (2022)
- [Prompt Tuning Pushes Farther, Contrastive Learning Pulls Closer: A Two-Stage Approach to Mitigate Social Biases](https://mlsanity.com/paper/2307.01595/) (2023)
- [Improved Representation Steering for Language Models](https://mlsanity.com/paper/2505.20809/) (2025)
- [Decomposing and Editing Predictions by Modeling Model Computation](https://mlsanity.com/paper/2404.11534/) (2024)
- [Attribute-to-Delete: Machine Unlearning via Datamodel Matching](https://mlsanity.com/paper/2410.23232/) (2024)
- [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)
- [Analyzing Finetuning Representation Shift for Multimodal LLMs Steering](https://mlsanity.com/paper/2501.03012/) (2025)

## Abstract (arXiv)

Modern neural models trained on textual data rely on pre-trained representations that emerge without direct supervision. As these representations are increasingly being used in real-world applications, the inability to control their content becomes an increasingly important problem. We formulate the problem of identifying and erasing a linear subspace that corresponds to a given concept, in order to prevent linear predictors from recovering the concept. We model this problem as a constrained, linear maximin game, and show that existing solutions are generally not optimal for this task. We derive a closed-form solution for certain objectives, and propose a convex relaxation, method, that works well for others. When evaluated in the context of binary gender removal, the method recovers a low-dimensional subspace whose removal mitigates bias by intrinsic and extrinsic evaluation. We show that the method is highly expressive, effectively mitigating bias in deep nonlinear classifiers while maintaining tractability and interpretability.