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This paper introduces MANCE, a novel method for concept erasure that leverages the Manifold Constraint Hypothesis (MCH) to effectively remove a target concept from representations while preserving correlated information. By projecting updates onto a lower-dimensional manifold estimated from natural inputs, MANCE iteratively refines representations based on classifier signals, demonstrating significant improvements across 119 evaluation settings in both text and vision tasks. The results reveal that MANCE and its enhancements, MANCE+ and MANCE++, achieve state-of-the-art performance in nonlinear concept erasure, validating the hypothesis that constrained interventions yield better preservation of information.
MANCE shows that constraining concept erasure updates to a natural representation manifold can dramatically enhance information preservation, achieving state-of-the-art results in nonlinear scenarios.
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.