A Kolmogorov-Arnold Neural Model for Cascading Extremes

This paper addresses the growing concern of cascading extreme events, such as an extreme earthquake followed by a tsunami, by presenting a novel method for risk assessment focused on these domino effects. The proposed approach develops an extreme value theory framework within a Kolmogorov-Arnold network (KAN) to estimate the probability of one extreme event triggering another, conditionally on a feature vector. An extra layer is added to the KAN architecture to ensure that the parameter of interest lies within the unit interval, and we refer to the resulting neural model as KANE (KAN with Natural Enforcement). The proposed method is backed by exhaustive numerical studies and further illustrated with real-world applications to seismology and climatology.

💡 Research Summary

This paper tackles the problem of quantifying and predicting cascading extreme events—situations where one extreme phenomenon (the “trigger”) induces another extreme phenomenon (the “follow‑up”). The authors introduce a new statistical‑machine‑learning framework that combines extreme‑value theory (EVT) with Kolmogorov‑Arnold Networks (KAN).

The core probabilistic object is the “α functional”, defined as the limit of the conditional probability that a binary follow‑up event I equals one given that a trigger variable Y exceeds a high threshold u. Formally, α = lim_{u→y*} P(I_u = 1 | Y > u). This functional generalizes the classical tail‑dependence coefficient and captures the probability of a cascade. By conditioning on a covariate vector x ∈