Markovianity of saddle‑to‑saddle transitions

Ascertain whether the sequence of saddle points visited during gradient flow training in networks defined by Equation (1) is Markovian—i.e., whether the next saddle can be inferred solely from the current one independent of earlier saddles.

Background

Understanding whether saddle visitation is Markovian would clarify the memory dependence of stage-like learning and facilitate predictive models of progression through the hierarchy of saddles.

The authors note that certain heteroclinic networks are known to be non-Markovian in dynamical systems, but the status in neural training dynamics remains unresolved.