arXiv:2606. 07782v1 Announce Type: cross Abstract: We propose a new framework for optimisation over non-Archimedean spaces inspired by Berkovich geometry.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
arXiv:2510.26266v3 Announce Type: replace Abstract: The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a p...
The paper demonstrates that the common-geodesic condition—where every output triple shares a geodesic point in a metric—does not ensure Fisher consistency for the structured SVM with the standard coordinate-wise argmax decoder. It presents minimal counterexamples, including a four-output star and a tree-metric classification, showing that only path-shaped trees maintain argmax consistency. The study also identifies the smallest full-support counterexamples and provides exact primal-dual certificates for all optimality claims.
The paper introduces a method for approximate vector search in ultrametric (infinity-metric) spaces by using a projection operator that transforms arbitrary dissimilarity functions into ultrametric ones while preserving nearest neighbors. It extends this approach to q-metric spaces, where triangle inequalities involve q-th powers, and learns an efficient approximation of the projected distances. Experiments show that higher q values speed up search at the cost of recall, yet the proposed methods remain competitive with existing search techniques.
arXiv:2610. 22592v1 Announce Type: cross Abstract: Empirical averages are fundamental statistical primitives.
arXiv:2605. 09916v2 Announce Type: replace-cross Abstract: We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal transport in large-scale, non-Euclidean datasets.
Quantifying the diversity of a set of objects is a fundamental problem in machine learning and statistics. Mironov and Prokhorenkova (2025) recently showed that three axioms-monotonicity, uniqueness,...