Extreme First-Passage Time of Many Interacting Particles

What the math gives to ML

The paper provides a sharp mechanism for how interactions alter extreme first-passage times in many-particle stochastic systems. Its no-go theorem says that broad bounded interactions with controlled short-time drift retain the independent-searcher logarithmic extreme-time scale, while coherent deterministic force accumulation can reach an inverse-population scale and stochastic pairwise forcing can achieve an additional logarithmic gain, 1/(N ln N). This transfers naturally to population-based neural-network optimization or inference, where success is defined by the first particle reaching a target loss or reward threshold. The key experiment is to implement several interaction regimes and test whether measured first-hit times exhibit the predicted 1/ln N, 1/N, or 1/(N ln N) scaling.