135 citations · 282 across the 11 of their papers we have counts for
5 papers · 1 filter
Function-Space Optimality of Neural Architectures with Multivariate Nonlinearities
Rahul Parhi, Michael Unser
We investigate the function-space optimality (specifically, the Banach-space optimality) of a large class of shallow neural architectures with multivariate nonlinearities/activatio…
Distributional Extension and Invertibility of the -Plane Transform and Its Dual
Rahul Parhi, Michael Unser
We investigate the distributional extension of the -plane transform in and of related operators. We parameterize the -plane domain as the Cartesian product of…
Weighted variation spaces and approximation by shallow ReLU networks
Ronald DeVore, Robert D. Nowak, Rahul Parhi +1
We investigate the approximation of functions on a bounded domain by the outputs of single-hidden-layer ReLU neural networks of width . This form of…
Variation Spaces for Multi-Output Neural Networks: Insights on Multi-Task Learning and Network Compression
Joseph Shenouda, Rahul Parhi, Kangwook Lee +1
This paper introduces a novel theoretical framework for the analysis of vector-valued neural networks through the development of vector-valued variation spaces, a new class of repr…
Deep Learning Meets Sparse Regularization: A Signal Processing Perspective
Rahul Parhi, Robert D. Nowak
Deep learning has been wildly successful in practice and most state-of-the-art machine learning methods are based on neural networks. Lacking, however, is a rigorous mathematical t…