9 papers
Kernel Methods for Learning Operators with Multiple Inputs and Outputs
Adrien Weihs, Chunyang Liao, Jingmin Sun +1
Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning. We introduce a general kernel-based encoder-decoder framework for oper…
Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning
Adrien Weihs, Hayden Schaeffer
We study the approximation and statistical complexity of learning collections of operators in a shared multi-task setting, with a focus on the Multiple Neural Operators (MNO) archi…
Generalization Bounds and Statistical Guarantees for Multi-Task and Multiple Operator Learning with MNO Networks
Adrien Weihs, Hayden Schaeffer
Multiple operator learning concerns learning operator families indexed by an operator descriptor . Training data are collected hierarchically by sampl…
Higher-Order Regularization Learning on Hypergraphs
Adrien Weihs, Andrea L. Bertozzi, Matthew Thorpe
Higher-Order Hypergraph Learning (HOHL) was recently introduced as a principled alternative to classical hypergraph regularization, enforcing higher-order smoothness via powers of…
A Deep Learning Framework for Multi-Operator Learning: Architectures and Approximation Theory
Adrien Weihs, Jingmin Sun, Zecheng Zhang +1
While many problems in machine learning focus on learning mappings between finite-dimensional spaces, scientific applications require approximating mappings between function spaces…
Topology-Aware Active Learning on Graphs
Harris Hardiman-Mostow, Jack Mauro, Adrien Weihs +1
We propose a graph-topological approach to active learning that directly targets the core challenge of exploration versus exploitation under scarce label budgets. To guide explorat…
Analysis of Semi-Supervised Learning on Hypergraphs
Adrien Weihs, Andrea L. Bertozzi, Matthew Thorpe
Hypergraphs provide a natural framework for modeling multiway interactions. We analyze a class of variational semi-supervised learning problems posed on random geometric hypergraph…
Discrete-to-Continuum Rates of Convergence for -Laplacian Regularization
Adrien Weihs, Jalal Fadili, Matthew Thorpe
Higher-order regularization problem formulations are popular frameworks used in machine learning, inverse problems and image/signal processing. In this paper, we consider the compu…
Consistency of Fractional Graph-Laplacian Regularization in Semi-Supervised Learning with Finite Labels
Adrien Weihs, Matthew Thorpe
Laplace learning is a popular machine learning algorithm for finding missing labels from a small number of labelled feature vectors using the geometry of a graph. More precisely, L…