[2602.23528] Neural Operators Can Discover Functional Clusters

Computer Science > Machine Learning arXiv:2602.23528 (cs) [Submitted on 26 Feb 2026] Title:Neural Operators Can Discover Functional Clusters Authors:Yicen Li, Jose Antonio Lara Benitez, Ruiyang Hong, Anastasis Kratsios, Paul David McNicholas, Maarten Valentijn de Hoop View a PDF of the paper titled Neural Operators Can Discover Functional Clusters, by Yicen Li and 5 other authors View PDF HTML (experimental) Abstract:Operator learning is reshaping scientific computing by amortizing inference across infinite families of problems. While neural operators (NOs) are increasingly well understood for regression, far less is known for classification and its unsupervised analogue: clustering. We prove that sample-based neural operators can learn any finite collection of classes in an infinite-dimensional reproducing kernel Hilbert space, even when the classes are neither convex nor connected, under mild kernel sampling assumptions. Our universal clustering theorem shows that any $K$ closed classes can be approximated to arbitrary precision by NO-parameterized classes in the upper Kuratowski topology on closed sets, a notion that can be interpreted as disallowing false-positive misclassifications. Building on this, we develop an NO-powered clustering pipeline for functional data and apply it to unlabeled families of ordinary differential equation (ODE) trajectories. Discretized trajectories are lifted by a fixed pre-trained encoder into a continuous feature map and mapped to soft as...