PreprintCC BY 4.0arXiv
Gaussian equivalence for CNN with non-Gaussian weights
Abstract
We study the infinite-width limit of convolutional neural networks with random weights and show that the Gaussian process limit does not require Gaussian priors. Assuming that the weights are i.i.d., centered, and have sufficiently many finite moments, converges weakly in the space of continuous functions on the compact input set to independent copies of a centered Gaussian process. Our framework accommodates activation functions of polynomial growth together with a broad class of patch-extraction operators, covering standard convolutions, padding, stride, and common pooling mechanisms.
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BibTeX
@misc{bassetti2026gaussian,
title = {{Gaussian equivalence for CNN with non-Gaussian weights}},
author = {Federico Bassetti and Vassili De Palma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25928},
eprint = {2610.25928},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25928},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gaussian equivalence for CNN with non-Gaussian weights
AU - Federico Bassetti
AU - Vassili De Palma
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25928
UR - https://arxiv.org/abs/2610.25928
AB - We study the infinite-width limit of convolutional neural networks with random weights and show that the Gaussian process limit does not require Gaussian priors. Assuming that the weights are i.i.d., centered, and have sufficiently many finite moments, converges weakly in the space of continuous functions on the compact input set to independent copies of a centered Gaussian process. Our framework accommodates activation functions of polynomial growth together with a broad class of patch-extraction operators, covering standard convolutions, padding, stride, and common pooling mechanisms.
ER -