# Large and moderate deviations for Gaussian neural networks

arxiv（2024）

Abstract

We prove large and moderate deviations for the output of Gaussian fully
connected neural networks. The main achievements concern deep neural networks
(i.e., when the model has more than one hidden layer) and hold for bounded and
continuous pre-activation functions. However, for deep neural networks fed by a
single input, we have results even if the pre-activation is ReLU. When the
network is shallow (i.e., there is exactly one hidden layer) the large and
moderate principles hold for quite general pre-activations and in an
infinite-dimensional setting.

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