VectorAdamforRotationEquivariant GeometryOptimization

Atthesame time, thedevelopment ofequivariant methods, which preservetheir output under the action of rotation or some other transformation, has proven to be important for geometry problems across these domains. In this work, we observethat Adam -- when treated as afunction that maps initial conditions to optimized results --isnotrotation equivariant forvector-valued parameters due to per-coordinate moment updates. This leads to significant artifacts and biases in practice.