MANCE: Manifold Aware Concept Erasure
MANCE leverages manifold constraints for nonlinear concept erasure, significantly reducing information leakage while preserving other concepts.
Key Findings
Methodology
The proposed MANCE method is based on the manifold constraint hypothesis, which posits that natural neural representations lie on a low-dimensional, structured manifold. It estimates the local tangent space of this manifold via PCA on neighboring natural representations. During concept erasure, the gradient signal from a classifier predicting the target concept is projected onto this tangent space, reweighted by local singular values, and used to iteratively update the representations. This approach combines nonlinear probes, local geometric estimation, and iterative refinement, supporting effective removal of complex, nonlinear concepts across text and vision tasks. Extensive experiments across 119 settings—including 13 language models and 40 CelebA-CLIP attributes—demonstrate consistent improvements over baseline methods like INLP, LEACE, and Obliviator, with leakage reductions exceeding 20pp and minimal control concept damage.
Key Results
- MANCE achieves an average leakage reduction of over 20 percentage points across diverse models and datasets, outperforming prior methods such as INLP and LEACE. When combined with preprocessing variants like MANCE++ (which includes closed-form linear and covariance matching steps), the method reaches state-of-the-art nonlinear concept erasure performance. In NLP tasks, leakage drops from 15-16pp to below 2pp, while in vision tasks, attribute leakage is reduced close to chance levels. The iterative nature and local manifold projection enable robust, scalable, and precise concept removal, especially for complex nonlinear attributes like gender and toxicity.
- Across 119 experimental settings, the approach consistently maintains control concept integrity, with control accuracy degradation kept below 5pp in most cases. The method demonstrates high coverage, successfully performing within specified surgicality budgets in over 90% of settings. Ablation studies confirm that the manifold projection step significantly enhances surgicality without sacrificing erasure effectiveness. The results validate the manifold constraint hypothesis, showing that interventions constrained to the natural representation manifold outperform unconstrained approaches.
- The experiments also reveal that the local tangent space estimation remains stable across different models and data regimes, supporting the hypothesis that natural representations cluster on a low-dimensional manifold. The combination of local geometric estimation and gradient projection provides a flexible, theoretically grounded framework for nonlinear concept erasure, opening avenues for more transparent and controllable AI systems.
Significance
This work advances the field of model interpretability and fairness by providing a principled, geometric approach to concept removal. Unlike linear methods, MANCE effectively handles complex, nonlinear attributes, making it applicable to real-world scenarios like bias mitigation and sensitive information removal. Its scalability and robustness across diverse models and modalities highlight its potential for broad adoption in AI safety, fairness, and transparency efforts. By grounding interventions in the natural representation manifold, the method offers a theoretically sound and practically effective tool for responsible AI development, addressing long-standing challenges in model interpretability and control.
Technical Contribution
The key technical innovation is the integration of local manifold estimation via PCA with gradient-based concept erasure. The method projects the concept classifier’s gradient onto the estimated tangent space, reweights it by local singular values, and applies a constrained update that remains within the natural representation manifold. The development of a closed-form solution for per-sample step sizes ensures local tangent-based updates are both effective and stable. The introduction of variants like MANCE+ and MANCE++—which incorporate linear preprocessing steps—further improves erasure quality and control-surgicality tradeoffs. The framework supports nonlinear, multi-round, and multimodal concept removal, representing a significant step beyond prior linear and kernel-based methods.
Novelty
This research is the first to formalize and operationalize the manifold constraint hypothesis for concept erasure, emphasizing the importance of constraining interventions to the natural representation manifold. Unlike prior linear methods (INLP, LEACE), MANCE supports nonlinear, iterative updates guided by local geometric estimates. Its innovative use of tangent space projection and local PCA distinguishes it from existing approaches, providing both theoretical guarantees and practical improvements. The combination of nonlinear probes, local geometry, and iterative refinement constitutes a novel framework for robust, scalable nonlinear concept removal.
Limitations
- The method relies on accurate local manifold estimation; errors in tangent space approximation can reduce erasure effectiveness, especially in high-dimensional or highly nonlinear regions.
- Computational overhead is significant due to repeated PCA, gradient projection, and iterative updates, limiting real-time or large-scale deployment.
- The approach assumes the natural representations lie on a low-dimensional manifold, which may not hold in all models or data regimes, potentially impacting generalizability.
Future Work
Future directions include developing more efficient local manifold estimation techniques, possibly leveraging deep learning-based geometric encodings. Extending the framework to online or adaptive settings for dynamic concept control, and exploring multi-concept erasure simultaneously, are promising avenues. Additionally, integrating the approach with explainability tools and fairness metrics can enhance transparency and trustworthiness. Further theoretical analysis of the manifold assumption in various model architectures and data distributions will solidify the framework's foundations and expand its applicability.
AI Executive Summary
Deep neural networks encode a multitude of attributes within their high-dimensional representations, often entangled and nonlinear in nature. Traditional concept erasure methods like INLP and LEACE, which rely on linear projections, struggle to effectively remove complex, nonlinear attributes without damaging other encoded information. To address this, the authors propose MANCE, a novel framework grounded in the manifold hypothesis, which posits that natural representations lie on a low-dimensional, structured manifold. By estimating the local tangent space of this manifold through PCA on neighboring natural inputs, MANCE constrains gradient-based updates to remain within this geometric structure.
The core innovation lies in projecting the gradient signals from a classifier predicting the target concept onto the estimated tangent space, reweighting these directions based on local singular values, and iteratively updating the representations. This process ensures that interventions do not push representations off the natural data manifold, thereby preserving other encoded concepts and reducing unintended damage. The method supports multiple rounds of refinement, enabling the effective removal of complex, nonlinear concepts such as gender, toxicity, and sycophancy across diverse models and modalities.
Extensive experiments demonstrate that MANCE consistently outperforms existing baselines, achieving over 20pp reduction in concept leakage while maintaining control concept integrity within 5pp. Its variants, MANCE+ and MANCE++, incorporate preprocessing steps like linear moment removal and covariance matching, further enhancing performance. The results validate the manifold constraint hypothesis, emphasizing the importance of geometric considerations in model interventions. This work paves the way for more transparent, controllable AI systems, with broad implications for fairness, safety, and interpretability. Future research will focus on improving scalability, extending to online settings, and integrating with explainability frameworks, promising a new paradigm in responsible AI development.
Deep Dive
Abstract
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.