Explicit integral representations and quantitative bounds for two-layer ReLU networks
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Abstract (arXiv)
An approach to construct explicit integral representations for two-layer ReLU networks is presented, which provides relatively simple representations for any multivariate polynomial. Quantitative bounds are provided for a particular, sharpened ReLU integral representation, which involves a harmonic extension and a projection. The bounds demonstrate that functions can be approximated with L2(D) errors that do not depend explicitly on dimension or degree, but rather the coefficients of their monomial expansions and the distribution D. We also present a connection to the RKHS of the exponential kernel K(x,y)=expleft(leftlangle x,yrightrangle right), and a very simple integral representation involving additionally multiplication via a fixed function which has better quantitative bounds.
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References · 10
- 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
- 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
- 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 422
- 2014Breaking the Curse of Dimensionality with Convex Neural Networkscited by 329
- 2019Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limitcited by 187
- 2019How do infinite width bounded norm networks look in function space?cited by 105
- 2015Neural Network with Unbounded Activation Functions is Universal Approximatorcited by 63
- 2019Neural tangent kernels, transportation mappings, and universal approximationcited by 30
- 2021On the Approximation Power of Two-Layer Networks of Random ReLUscited by 29
- 2019Neural network integral representations with the ReLU activation functioncited by 8
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