Traveling fronts in a spatial epidemic model with slow loss of immunity
arXiv:2608.04594
2026
Dynamics
1 ideas extracted · analyzed Aug 31, 2026
What the math gives to ML
The paper provides a constructive entry-exit mechanism for slow-fast traveling fronts: a trajectory can remain near a critical manifold even after the instantaneous transverse eigenvalue changes sign, and exits only when accumulated transverse growth reaches zero. The quantitative condition is an integral of the weak eigenvalue along the slow flow, rather than a pointwise stability test. This mechanism can transfer to neural-network optimization by treating curvature or gradient-noise statistics as a slow state and using an accumulated transverse-growth budget to decide when to leave an exploratory high-step regime. The key falsifiable prediction is a delayed transition whose switching time is determined by an integral crossing.
Ideas from this paper
✗ Failed on benchmark
2026
Replace pointwise curvature-based learning-rate decisions with a slow-fast entry-exit scheduler. The optimizer maintains a slowly varying state representing effective curvature or gradient-noise level, accumulates the weak transverse growth rate along that slow trajectory, and changes learning regime only when the accumulated rate returns to zero. This permits controlled passage through locally unstable or poorly conditioned regions while preventing indefinite residence in a regime with net…
Useful7/10
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