# Better Hit the Nail on the Head than Beat around the Bush: Removing Protected Attributes with a Single Projection

arXiv: https://arxiv.org/abs/2212.04273 · HTML: https://mlsanity.com/paper/2212.04273/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 39 references that are in the map.
- First posted on arXiv 8 Dec 2022.

## Builds on (most cited first, 27 of 27)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [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)
- [Bag of Tricks for Efficient Text Classification](https://mlsanity.com/paper/1607.01759/) (2016)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Gender Bias in Coreference Resolution: Evaluation and Debiasing Methods](https://mlsanity.com/paper/1804.06876/) (2018)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [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)
- [SimLex-999: Evaluating Semantic Models with (Genuine) Similarity Estimation](https://mlsanity.com/paper/1408.3456/) (2014)
- [Learning Gender-Neutral Word Embeddings](https://mlsanity.com/paper/1809.01496/) (2018)
- [Harms of Gender Exclusivity and Challenges in Non-Binary Representation in Language Technologies](https://mlsanity.com/paper/2108.12084/) (2021)
- [Linear Adversarial Concept Erasure](https://mlsanity.com/paper/2201.12091/) (2022)
- [Understanding Undesirable Word Embedding Associations](https://mlsanity.com/paper/1908.06361/) (2019)
- [What's in a Name? Reducing Bias in Bios without Access to Protected Attributes](https://mlsanity.com/paper/1904.05233/) (2019)
- [OSCaR: Orthogonal Subspace Correction and Rectification of Biases in Word Embeddings](https://mlsanity.com/paper/2007.00049/) (2020)
- [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)
- [Exploring the Linear Subspace Hypothesis in Gender Bias Mitigation](https://mlsanity.com/paper/2009.09435/) (2020)
- [Unit Testing for Concepts in Neural Networks](https://mlsanity.com/paper/2208.10244/) (2022)
- [How Conservative are Language Models? Adapting to the Introduction of Gender-Neutral Pronouns](https://mlsanity.com/paper/2204.10281/) (2022)
- [Analyzing Gender Representation in Multilingual Models](https://mlsanity.com/paper/2204.09168/) (2022)
- [The Rediscovery Hypothesis: Language Models Need to Meet Linguistics](https://mlsanity.com/paper/2103.01819/) (2021)
- [Firearms and Tigers are Dangerous, Kitchen Knives and Zebras are Not: Testing whether Word Embeddings Can Tell](https://mlsanity.com/paper/1809.01375/) (2018)
- [Obstructing Classification via Projection](https://mlsanity.com/paper/2105.09047/) (2021)

## Built on by (most cited first, 17 of 17)

- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [Convergent Linear Representations of Emergent Misalignment](https://mlsanity.com/paper/2506.11618/) (2025)
- [On Behalf of the Stakeholders: Trends in NLP Model Interpretability in the Era of LLMs](https://mlsanity.com/paper/2407.19200/) (2024)
- [COSMIC: Generalized Refusal Direction Identification in LLM Activations](https://mlsanity.com/paper/2506.00085/) (2025)
- [RepIt: Steering Language Models with Concept-Specific Refusal Vectors](https://mlsanity.com/paper/2509.13281/) (2025)
- [Fundamental Limits of Perfect Concept Erasure](https://mlsanity.com/paper/2503.20098/) (2025)
- [Preserving Task-Relevant Information Under Linear Concept Removal](https://mlsanity.com/paper/2506.10703/) (2025)
- [Improving Causal Interventions in Amnesic Probing with Mean Projection or LEACE](https://mlsanity.com/paper/2506.11673/) (2025)
- [Can Large Language Models (or Humans) Disentangle Text?](https://mlsanity.com/paper/2403.16584/) (2024)
- [Quiet Feature Learning in Algorithmic Tasks](https://mlsanity.com/paper/2505.03997/) (2025)
- [Suppression Is Not Forgetting: Residual Recoverability in Visual Concept Unlearning for VLMs](https://mlsanity.com/paper/2604.03114/) (2026)
- [SkillEval: Decomposing Agent Skill Quality into Interpretable Signals](https://mlsanity.com/paper/2608.06891/) (2026)
- [Iterative Erasure Count Is Not an Affine-Invariant Concept Dimension](https://mlsanity.com/paper/2608.10566/) (2026)
- [What Happens to a Dataset Transformed by a Projection-based Concept Removal Method?](https://mlsanity.com/paper/2403.16142/) (2024)
- [Balancing the Scales: Reinforcement Learning for Fair Classification](https://mlsanity.com/paper/2407.10629/) (2024)
- [Calibrating Post-Training Feature Shifts for LLM Data Contamination Detection](https://mlsanity.com/paper/2608.10462/) (2026)

## Abstract (arXiv)

Bias elimination and recent probing studies attempt to remove specific information from embedding spaces. Here it is important to remove as much of the target information as possible, while preserving any other information present. INLP is a popular recent method which removes specific information through iterative nullspace projections. Multiple iterations, however, increase the risk that information other than the target is negatively affected. We introduce two methods that find a single targeted projection: Mean Projection (MP, more efficient) and Tukey Median Projection (TMP, with theoretical guarantees). Our comparison between MP and INLP shows that (1) one MP projection removes linear separability based on the target and (2) MP has less impact on the overall space. Further analysis shows that applying random projections after MP leads to the same overall effects on the embedding space as the multiple projections of INLP. Applying one targeted (MP) projection hence is methodologically cleaner than applying multiple (INLP) projections that introduce random effects.