Time-delayed feedback turns Arrhenius escape logarithmic
arXiv:2608.30624
2026
Dynamics
2 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper provides a transferable delayed-feedback mechanism that changes noise-activated escape from Arrhenius scaling, proportional to exp(Delta U divided by D), to logarithmic scaling after a delay-induced instability. Linearization gives a computable stability boundary, k times tau equals pi over 2, where k is the local restoring curvature. Beyond this boundary, stochastic fluctuations are amplified by an unstable delay mode until they reach an escape boundary, suggesting a controlled delayed-gradient phase for escaping sharp or stagnant optimization basins. The mechanism is most useful as a bounded optimizer burst with curvature-based delay selection and an automatic stop condition.
Ideas from this paper
✗ Failed on benchmark
2026
Add a controllable delay to the gradient force during optimization so that parameters follow a delayed-gradient dynamical system. Choose the delay below the stability boundary for ordinary training, and temporarily cross the boundary when the optimizer is trapped in a sharp or stagnant basin, causing stochastic fluctuations to be amplified out of the basin rather than waiting for a rare Arrhenius escape.
Useful8/10
Difficulty6/10
Novelty7/10
✗ Failed on benchmark
2026
Use the paper's extreme-value escape statistics as a diagnostic for delayed-gradient bursts. If many stochastic minibatch realizations escape through an unstable delay mode, their first-passage times should become approximately Gumbel distributed, allowing the optimizer to distinguish useful basin escape from destructive divergence and to terminate or retune the burst automatically.
Useful7/10
Difficulty5/10
Novelty8/10