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

We investigate properties of neural networks that use both ReLU and $x^2$ asactivation functions and build upon previous results to show that both analyticfunctions and functions in Sobolev spaces can be approximated by such networksof constant depth to arbitrary accuracy, demonstrating optimal orderapproximation rates across all nonlinear approximators, including standard ReLUnetworks. We then show how to leverage low local dimensionality in somecontexts to overcome the curse of dimensionality, obtaining approximation ratesthat are optimal for unknown lower-dimensional subspaces.

Optimal Approximation Complexity of High-Dimensional Functions with Neural Networks