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About this paper
Alberto Bordino, Stefano Favaro, Sandra Fortini
The authors use a second-order Poincaré inequality on neural-network outputs as functions of Gaussian weights, calculating gradients and Hessians to bound their distance from Gaussian-process limits. For a shallow network, the bound scales as width⁻¹/²; for a two-hidden-layer network under smoothness and growth assumptions, it scales as width⁻¹/⁴. This slower rate describes the bound, not necessarily the network’s actual error.
Summary by alphaXiv.
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