Fundamental Limits of Perfect Concept Erasure

Concept erasure is the task of erasing information about a concept (e.g., gender or race) from a representation set while retaining the maximum possible utility -- information from original representations. Concept erasure is useful in several applications, such as removing sensitive concepts to achieve fairness and interpreting the impact of specific concepts on a model's performance. Previous concept erasure techniques have prioritized robustly erasing concepts over retaining the utility of the resultant representations. However, there seems to be an inherent tradeoff between erasure and retaining utility, making it unclear how to achieve perfect concept erasure while maintaining high utility. In this paper, we offer a fresh perspective toward solving this problem by quantifying the fundamental limits of concept erasure through an information-theoretic lens. Using these results, we investigate constraints on the data distribution and the erasure functions required to achieve the limits of perfect concept erasure. Empirically, we show that the derived erasure functions achieve the optimal theoretical bounds. Additionally, we show that our approach outperforms existing methods on a range of synthetic and real-world datasets using GPT-4 representations.