arXiv:2609.02665 2026 Sampling 1 ideas extracted · analyzed Sep 3, 2026
The paper gives a constructive asymptotic mechanism for Brownian survival in a wedge with partially reactive boundaries. Robin reactivity introduces a boundary length scale and produces a crossover between nearly reflecting behavior at short times and the absorbing-wedge persistence law at long times. The transferable asset is the Feynman-Kac representation of Robin killing through accumulated boundary local time, which can be used to build diffusion samplers with soft, calibrated constraint handling instead of hard rejection or arbitrary penalties. The predicted crossover scale and late-time power-law exponent provide falsifiable diagnostics for the neural implementation.
Train a score-based diffusion model on a domain with partially reactive constraints, replacing hard rejection or large boundary penalties by a Robin boundary condition. Samples approaching the constraint boundary acquire a hazard proportional to accumulated boundary local time, giving a continuous interpolation between reflection and absorption.