Volume preserving artificial neural network and system and method for building a volume preserving trainable artificial neural network

A method for generating and executing a trained volume-preserving artificial neural network, on one or more processors, the one or more processors in communication with a data storage, the method comprising:

• receiving, by the one or more processors, the input data at an input layer of the volume-preserving neural network;
• processing, by the one or more processors, the input data in sequentially connected volume-preserving hidden layers which are intermediate the input layer and a downsizing output layer, and outputting, by the one or more processors, the output at the downsizing output layer of the volume-preserving artificial neural network to the data storage, wherein the volume-preserving artificial neural network comprises:
• the input layer to receive the input data;
• the sequentially connected volume-preserving hidden layers to perform operations on the input data to address vanishing gradients or exploding gradients for artificial neural networks, the first hidden layer connected to the input layer, each hidden layer comprising:
• at least 2*┌log2(nin)┐ volume-preserving rotation sublayers, where nin is the number of inputs to the rotation sublayer;
• at least 2*┌log2(nin)┐ volume-preserving permutation sublayers, where nin is the number of inputs to the permutation sublayer;
• one or more volume-preserving diagonal sublayer;
• a volume-preserving activation sublayer comprising a grouped activation function acting on a grouping of input variables provided to the volume-preserving activation sublayer;
• and
• the downsizing output layer connected to the activation sublayer of the last hidden layer to downsize and output the received output from the activation sublayer as the output of the volume-preserving neural network.