arXiv:2608.02297 2026 Dynamics 1 ideas extracted · analyzed Aug 31, 2026
The paper provides a constructive non-Markovian resetting mechanism: at each event, the system is relocated to a state sampled uniformly from its entire past. Its ensemble evolution contains the history-average operator \(t^{-1}\int_0^t \rho(s)\,ds\), producing algebraic rather than exponential relaxation and a distinction between discrete-frequency and continuous-frequency systems. A direct neural-network transfer is a history-reset optimizer that occasionally replaces the current iterate by a uniformly sampled previous iterate, or adds a continuous-time pull toward the running historical average. The key falsifiable prediction is that this term suppresses an unstable quadratic mode when the reset rate exceeds its growth rate, while stable modes can acquire algebraic relaxation tails.
Augment gradient descent with stochastic relocations to uniformly sampled historical parameter vectors. In expectation, the optimizer receives a non-Markovian correction toward the running average of all previous iterates, which can suppress runaway directions and revisit earlier basins instead of remaining trapped in a sharp or unstable region.