New error bounds for deep networks using sparse grids

2017/12/23 by Hadrien Montanelli, Qiang Du, Montanelli, Hadrien +1 · 3 citations
Engineering · Computer Science · #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #Image and Signal Denoising Methods

paper · doi:10.48550/arxiv.1712.08688

Abstract

We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks. We present new error estimates for which the curse of the dimensionality is lessened by establishing a connection with sparse grids.

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• On the Dimension-Free Approximation of Deep Neural Networks for Symmetric Korobov Functions
• General transformation neural networks: A class of parametrized functions for high-dimensional function approximation
• Generalization Analysis for Classification on Korobov Space

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