# Gold Doesn't Always Glitter: Spectral Removal of Linear and Nonlinear Guarded Attribute Information

arXiv: https://arxiv.org/abs/2203.07893 · HTML: https://mlsanity.com/paper/2203.07893/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 21 of 21)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [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)
- [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)
- [FastText.zip: Compressing text classification models](https://mlsanity.com/paper/1612.03651/) (2016)
- [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)
- [Demographic Dialectal Variation in Social Media: A Case Study of African-American English](https://mlsanity.com/paper/1608.08868/) (2016)
- [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)
- [Learning Gender-Neutral Word Embeddings](https://mlsanity.com/paper/1809.01496/) (2018)
- [Black is to Criminal as Caucasian is to Police: Detecting and Removing Multiclass Bias in Word Embeddings](https://mlsanity.com/paper/1904.04047/) (2019)
- [Using millions of emoji occurrences to learn any-domain representations for detecting sentiment, emotion and sarcasm](https://mlsanity.com/paper/1708.00524/) (2017)
- [Linear Adversarial Concept Erasure](https://mlsanity.com/paper/2201.12091/) (2022)
- [Towards Robust and Privacy-preserving Text Representations](https://mlsanity.com/paper/1805.06093/) (2018)
- [Understanding Undesirable Word Embedding Associations](https://mlsanity.com/paper/1908.06361/) (2019)
- [Privacy-preserving Neural Representations of Text](https://mlsanity.com/paper/1808.09408/) (2018)
- [Diverse Adversaries for Mitigating Bias in Training](https://mlsanity.com/paper/2101.10001/) (2021)
- [Native Language Cognate Effects on Second Language Lexical Choice](https://mlsanity.com/paper/1805.09590/) (2018)

## Built on by (most cited first, 30 of 34)

- [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)
- [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)
- [Convergent Linear Representations of Emergent Misalignment](https://mlsanity.com/paper/2506.11618/) (2025)
- [Spectral Editing of Activations for Large Language Model Alignment](https://mlsanity.com/paper/2405.09719/) (2024)
- [Shielded Representations: Protecting Sensitive Attributes Through Iterative Gradient-Based Projection](https://mlsanity.com/paper/2305.10204/) (2023)
- [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)
- [Uncovering Intermediate Variables in Transformers using Circuit Probing](https://mlsanity.com/paper/2311.04354/) (2023)
- [How Reliable are Causal Probing Interventions?](https://mlsanity.com/paper/2408.15510/) (2024)
- [Understanding Reasoning in Chain-of-Thought from the Hopfieldian View](https://mlsanity.com/paper/2410.03595/) (2024)
- [FairImagen: Post-Processing for Bias Mitigation in Text-to-Image Models](https://mlsanity.com/paper/2510.21363/) (2025)
- [Erasure of Unaligned Attributes from Neural Representations](https://mlsanity.com/paper/2302.02997/) (2023)
- [Fundamental Limits of Perfect Concept Erasure](https://mlsanity.com/paper/2503.20098/) (2025)
- [From Emergence to Control: Probing and Modulating Self-Reflection in Language Models](https://mlsanity.com/paper/2506.12217/) (2025)
- [A Joint Matrix Factorization Analysis of Multilingual Representations](https://mlsanity.com/paper/2310.15513/) (2023)
- [Competence-Based Analysis of Language Models](https://mlsanity.com/paper/2303.00333/) (2023)
- [Preserving Task-Relevant Information Under Linear Concept Removal](https://mlsanity.com/paper/2506.10703/) (2025)
- [Explaining Text Classifiers with Counterfactual Representations](https://mlsanity.com/paper/2402.00711/) (2024)
- [Surgical Feature-Space Decomposition of LLMs: Why, When and How?](https://mlsanity.com/paper/2405.13039/) (2024)
- [Applying Intrinsic Debiasing on Downstream Tasks: Challenges and Considerations for Machine Translation](https://mlsanity.com/paper/2406.00787/) (2024)
- [Obliviator Reveals the Cost of Nonlinear Guardedness in Concept Erasure](https://mlsanity.com/paper/2603.07529/) (2026)
- [A framework for analyzing concept representations in neural models](https://mlsanity.com/paper/2605.01381/) (2026)
- [Log-linear Guardedness and its Implications](https://mlsanity.com/paper/2210.10012/) (2022)
- [Cross-Attention is Not Enough: Incongruity-Aware Dynamic Hierarchical Fusion for Multimodal Affect Recognition](https://mlsanity.com/paper/2305.13583/) (2023)
- [FALCON: Fine-grained Activation Manipulation by Contrastive Orthogonal Unalignment for Large Language Model](https://mlsanity.com/paper/2502.01472/) (2025)
- [Iterative Multilingual Spectral Attribute Erasure](https://mlsanity.com/paper/2506.11244/) (2025)
- [Iterative Erasure Count Is Not an Affine-Invariant Concept Dimension](https://mlsanity.com/paper/2608.10566/) (2026)
- [Advancing Fairness in Natural Language Processing: From Traditional Methods to Explainability](https://mlsanity.com/paper/2410.12511/) (2024)

## Abstract (arXiv)

We describe a simple and effective method (Spectral Attribute removaL; SAL) to remove private or guarded information from neural representations. Our method uses matrix decomposition to project the input representations into directions with reduced covariance with the guarded information rather than maximal covariance as factorization methods normally use. We begin with linear information removal and proceed to generalize our algorithm to the case of nonlinear information removal using kernels. Our experiments demonstrate that our algorithm retains better main task performance after removing the guarded information compared to previous work. In addition, our experiments demonstrate that we need a relatively small amount of guarded attribute data to remove information about these attributes, which lowers the exposure to sensitive data and is more suitable for low-resource scenarios. Code is available at https://github.com/jasonshaoshun/SAL.