English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

There is a growing interest on large-width asymptotic properties of Gaussianneural networks (NNs), namely NNs whose weights are initialized according toGaussian distributions. A well-established result is that, as the width goes toinfinity, a Gaussian NN converges in distribution to a Gaussian stochasticprocess, which provides an asymptotic or qualitative Gaussian approximation ofthe NN. In this paper, we introduce some non-asymptotic or quantitativeGaussian approximations of Gaussian NNs, quantifying the approximation errorwith respect to some popular distances for (probability) distributions, e.g.the $1$-Wasserstein distance, the total variation distance and theKolmogorov-Smirnov distance. Our results rely on the use of second-orderGaussian Poincar\'e inequalities, which provide tight estimates of theapproximation error, with optimal rates. This is a novel application ofsecond-order Gaussian Poincar\'e inequalities, which are well-known in theprobabilistic literature for being a powerful tool to obtain Gaussianapproximations of general functionals of Gaussian stochastic processes. Ageneralization of our results to deep Gaussian NNs is discussed.

Non-asymptotic approximations of Gaussian neural networks via second-order Poincar\'e inequalities