4 papers
A Closed-Form Formula for Consistent Lipschitz Regression on Metric Spaces with Sparse Neural Network Realizations
Ruiyang Hong, Hrad Ghoukasian, Anastasis Kratsios
Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions o…
Classification Fields: Arbitrarily Fine Recursive Hierarchical Clustering From Few Examples
Yicen Li, Ruiyang Hong, Anastasis Kratsios +2
Classical clustering methods usually return either a finite partition of the observed data or a finite dendrogram over it. This finite-sample view is inadequate when the hierarchy…
Neural Operators Can Discover Functional Clusters
Yicen Li, Jose Antonio Lara Benitez, Ruiyang Hong +3
Operator learning is reshaping scientific computing by amortizing inference across infinite families of problems. While neural operators (NOs) are increasingly well understood for…
Bridging the Gap Between Approximation and Learning via Optimal Approximation by ReLU MLPs of Maximal Regularity
Ruiyang Hong, Anastasis Kratsios
The foundations of deep learning are supported by the seemingly opposing perspectives of approximation or learning theory. The former advocates for large/expressive models that nee…