Recovering Discarded Geometric Symmetries for AI Privacy

Researchers have developed a novel framework to understand and recover geometric information that machine learning models implicitly discard, particularly when inputs are subject to Lie group actions (e.g., rotations, translations). The framework introduces two key concepts: the "null fiber," which identifies group elements whose inverse action on an input is undetectable by the model, and the "stabilizer," representing the largest subgroup under which the model's function remains invariant. The paper mathematically demonstrates that for smooth maps, null fibers always possess a significant dimension, regardless of the model's architecture. For compact groups, a spectral characterization of these objects is provided using the Peter-Weyl theorem. A significant finding is that these null fiber elements can be computed efficiently using Newton iteration, with a computational cost comparable to a few gradient evaluations. This efficiency makes the framework practically applicable. The research explores practical applications of this recovered geometric information, including data masking, which can obscure sensitive attributes while preserving relevant features for the model; model fingerprinting, to uniquely identify models; and privacy-preserving computation, by leveraging the symmetries the model ignores. Experimental validation on molecular property prediction under SO(3) and spherical image classification under the Möbius group demonstrates the framework's utility in real-world scenarios.