On the boundedness of infinite products of relaxed projections: perturbations resilience and dynamic string-averaging

What the math gives to ML

The paper provides a stability theory for infinite compositions of relaxed projections onto affine subspaces, including additive perturbations and dynamically changing string-averaging controls. The transferable asset is not projection itself, which is standard, but the combination of nonexpansive composition, bounded perturbation propagation, and explicit control over dynamically varying projection strings. This suggests constraint-enforcing neural modules that apply several learned or fixed affine projections in short strings, average the resulting states, and tolerate gradient noise or approximate projections. The strongest guarantees concern affine subspaces and suitably regular controls; arbitrary convex constraints with poorly controlled schedules can behave very differently.