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Found 8 papers, 1 papers with code
Function-Space Optimality of Neural Architectures With Multivariate Nonlinearities
We investigate the function-space optimality (specifically, the Banach-space optimality) of a large class of shallow neural architectures with multivariate nonlinearities/activation functions.
Weighted variation spaces and approximation by shallow ReLU networks
A new and more proper definition of model classes on domains is given by introducing the concept of weighted variation spaces.
Variation Spaces for Multi-Output Neural Networks: Insights on Multi-Task Learning and Network Compression
This representer theorem establishes that shallow vector-valued neural networks are the solutions to data-fitting problems over these infinite-dimensional spaces, where the network widths are bounded by the square of the number of training data.
Deep Learning Meets Sparse Regularization: A Signal Processing Perspective
Deep learning has been wildly successful in practice and most state-of-the-art machine learning methods are based on neural networks.
Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks
We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks.
What Kinds of Functions do Deep Neural Networks Learn? Insights from Variational Spline Theory
The function space consists of compositions of functions from the Banach spaces of second-order bounded variation in the Radon domain.
Banach Space Representer Theorems for Neural Networks and Ridge Splines
We derive a representer theorem showing that finite-width, single-hidden layer neural networks are solutions to these inverse problems.
The Role of Neural Network Activation Functions
A wide variety of activation functions have been proposed for neural networks.
