Dynamical phase transitions for single particles in the semiclassical and weak noise limits
arXiv:2609.01197
2026
Dynamics
1 ideas extracted · analyzed Sep 2, 2026
What the math gives to ML
The paper provides a transferable mechanism for detecting dynamical phase transitions through competition between return trajectories, rather than equilibrium free energies. Its central objects are a dynamical generating function, Fisher zeros that approach the physical time axis, and an order parameter distinguishing competing trajectory families. For neural networks, the most promising transfer is to treat an ensemble of stochastic optimization or inference trajectories as a finite-noise path ensemble and monitor a complexified return generating function. A zero approach or saddle-weight crossing could signal an abrupt change in basin occupancy and trigger learning-rate or noise scheduling.
Ideas from this paper
Unverified
2026
Run an ensemble of noisy optimization trajectories and regard trajectories that return to the same loss basin as competing dynamical phases. Estimate a complex return generating function from their path costs; a near-zero of this function signals cancellation between trajectory families and predicts an abrupt change in basin occupancy. Use the signal to reduce learning rate or optimizer noise near a transition, or increase noise when one phase dominates too early.
Useful6/10
Difficulty6/10
Novelty8/10