# MANCE: Manifold Aware Concept Erasure

arXiv: https://arxiv.org/abs/2607.03973 · HTML: https://mlsanity.com/paper/2607.03973/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 29 references that are in the map.
- First posted on arXiv 4 Jul 2026.

## Builds on (most cited first, 26 of 26)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [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)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Discovering Language Model Behaviors with Model-Written Evaluations](https://mlsanity.com/paper/2212.09251/) (2022)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [What you can cram into a single vector: Probing sentence embeddings for linguistic properties](https://mlsanity.com/paper/1805.01070/) (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)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [PKU-SafeRLHF: Towards Multi-Level Safety Alignment for LLMs with Human Preference](https://mlsanity.com/paper/2406.15513/) (2024)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Extracting Latent Steering Vectors from Pretrained Language Models](https://mlsanity.com/paper/2205.05124/) (2022)
- [Fine-grained Analysis of Sentence Embeddings Using Auxiliary Prediction Tasks](https://mlsanity.com/paper/1608.04207/) (2016)
- [Censoring Representations with an Adversary](https://mlsanity.com/paper/1511.05897/) (2015)
- [Assessing BERT's Syntactic Abilities](https://mlsanity.com/paper/1901.05287/) (2019)
- [Adversarial Removal of Demographic Attributes from Text Data](https://mlsanity.com/paper/1808.06640/) (2018)
- [Linear Adversarial Concept Erasure](https://mlsanity.com/paper/2201.12091/) (2022)
- [Representation Surgery: Theory and Practice of Affine Steering](https://mlsanity.com/paper/2402.09631/) (2024)
- [Kernelized Concept Erasure](https://mlsanity.com/paper/2201.12191/) (2022)
- [Shielded Representations: Protecting Sensitive Attributes Through Iterative Gradient-Based Projection](https://mlsanity.com/paper/2305.10204/) (2023)
- [A Practical Method for Generating String Counterfactuals](https://mlsanity.com/paper/2402.11355/) (2024)
- [Obliviator Reveals the Cost of Nonlinear Guardedness in Concept Erasure](https://mlsanity.com/paper/2603.07529/) (2026)

## Abstract (arXiv)

Concept erasure aims to remove a target concept from a representation while preserving the other information encoded in it. This is difficult because representations encode many concepts that are often correlated with the erasure target, so removing the target risks damaging them. We propose the Manifold Constraint Hypothesis (MCH): if natural representations concentrate on a structured, lower-dimensional manifold, then interventions should be constrained to that manifold and better preserve other information encoded in the representation during interventions. We instantiate MCH in a new concept erasure method: MANifold aware Concept Erasure (MANCE). MANCE performs iterative updates to the representations using signals from a classifier that predicts a target concept. We estimate the manifold using representations obtained from natural inputs, and then we project the concept removal update to the estimated manifold. We perform extensive evaluation on 119 settings spanning text and vision, including 13 language models, three NLP concepts, and 40 CelebA-CLIP attributes. Employing MANCE on top of previous methods shows consistent improved leakage results. We also introduce MANCE+ and MANCE++, which prepend a closed-form erasure algorithm before employing MANCE, achieving better leakage--surgicality tradeoffs relative to matched full-space updates. MANCE++, our best method, achieves state-of-the-art results on nonlinear concept erasure. These results support MCH in the erasure setting: interventions should be constrained to the natural representation manifold.