arXiv:2608.20276 2026 Sampling 1 ideas extracted · analyzed Sep 1, 2026
The paper provides a constructive transition-state mechanism for predicting recurrent events in a chaotic Hamiltonian system: define a dividing surface near a saddle orbit, count one-way phase-space flux through it, and use ergodicity to convert that flux into a mean event rate. The saddle-orbit surface is valuable because it suppresses rapid recrossings, producing a measurable gap in crossing-time statistics and enabling accurate rate prediction. A transferable neural-network analogue is to treat mode changes in energy-based or diffusion models as basin-transition events, estimate one-way flux through learned saddle-oriented surfaces, and adapt temperature or noise until the measured transition rate matches a target rather than tuning noise blindly.
Use a learned dividing surface between two modes or basins of a neural energy model, and regulate Langevin or diffusion noise using the measured one-way crossing flux. The surface should be aligned with an estimated saddle direction and should reject immediate recrossings, so the controller responds to genuine mode transitions rather than local oscillations.