New work on arXiv (2610.25191) examines first-exit prediction for momentum SGD. The authors compare strongly convex finite pools that share identical pointwise gradient laws and matched iid momentum dynamics. Despite those similarities, the pools can behave differently once reshuffled, indicating that first-exit behavior depends on sampling information that pointwise laws omit.
Pointwise gradient laws describe the gradient at each point but not the order in which samples are drawn. The study suggests this sampling structure, along with curvature, matters for when momentum SGD leaves a region. The abstract does not provide full experimental details, but the claim is direct: matching pointwise laws and momentum dynamics is not enough to match first-exit predictions.