Deep neural networks are notorious for defying theoretical treatment. However, when the number of parameters in each layer tends to infinity, the network function is a Gaussian process (GP) and quantitatively predictive description is possible. Gaussian approximation allows one to formulate criteria for selecting hyperparameters, such as variances of weights and biases, as well as the learning rate. These criteria rely on the notion of criticality defined for deep neural networks. In this work we describe a new practical way to diagnose criticality.

Deep neural networks are notorious for defying theoretical treatment.

Deep neural networks are notorious for defying theoretical treatment. However, when the number of parameters in each layer tends to infinity, the network function is a Gaussian process (GP) and quantitatively predictive description is possible. Gaussian approximation allows one to formulate criteria for selecting hyperparameters, such as variances of weights and biases, as well as the learning rate. These criteria rely on the notion of criticality defined for deep neural networks. In this work we describe a new practical way to diagnose criticality.

Deep neural networks are notorious for defying theoretical treatment. However, when the number of parameters in each layer tends to infinity the network function is a Gaussian process (GP) and quantitatively predictive description is possible. Gaussian approximation allows to formulate criteria for selecting hyperparameters, such as variances of weights and biases, as well as the learning rate. These criteria rely on the notion of criticality defined for deep neural networks. In this work we describe a new way to diagnose (both theoretically and empirically) this criticality. To that end, we introduce partial Jacobians of a network, defined as derivatives of preactivations in layer $l$ with respect to preactivations in layer $l_0