Achieving Approximate Symmetry Is Exponentially Easier than Exact Symmetry

ArXi:2512.11855v2 Announce Type: replace Enforcing exact symmetry in machine learning models often yields significant gains in scientific applications, serving as a powerful inductive bias. However, recent work suggests that relying on approximate symmetry can offer greater flexibility and robustness. Despite promising empirical evidence, there has been little theoretical understanding, and in particular, a direct comparison between exact and approximate symmetry is missing from the literature.