symmetry-discovery

This paper studies adaptive symmetry discovery for dynamical system identification, showing that known symmetries reduce the trajectory length needed for identification and proposing a method to learn unknown symmetry groups from a single trajectory to achieve the same optimal length.

This paper introduces the ⋆_G tensor algebra, a framework that makes equivariance an intrinsic algebraic property rather than an architectural constraint, providing provably-optimal symmetry-preserving tensor approximation, Kronecker factorization for composing multiple symmetries, and a Lean 4 formalization. Experiments on QM9 molecular geometry demonstrate data-driven discovery of physical symmetry selection rules.