Large and moderate deviations for Gaussian Neural Networks

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. Joint work with Barbara Pacchiarotti (Univ. Roma Tor Vergata) and Gianluca Torrisi (IAC-CNR).