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# Linear Adversarial Concept Erasure

*Proceedings of the 39th International Conference on Machine Learning*, PMLR 162:18400-18421, 2022.

#### Abstract

Modern neural models trained on textual data rely on pre-trained representations that emerge without direct supervision. As these representations are increasingly being used in real-world applications, the inability to

*control*their content becomes an increasingly important problem. In this work, we formulate the problem of identifying a linear subspace that corresponds to a given concept, and removing it from the representation. We formulate this problem as a constrained, linear minimax game, and show that existing solutions are generally not optimal for this task. We derive a closed-form solution for certain objectives, and propose a convex relaxation that works well for others. When evaluated in the context of binary gender removal, the method recovers a low-dimensional subspace whose removal mitigates bias by intrinsic and extrinsic evaluation. Surprisingly, we show that the method—despite being linear—is highly expressive, effectively mitigating bias in the output layers of deep, nonlinear classifiers while maintaining tractability and interpretability.