Abstract: A computer-implemented method comprising: processing data in a neural network to compute a network tensor comprising a plurality of tensor elements represented in an initial numerical format; computing a histogram of tensor elements; selecting a target numerical format, the target numerical format having a lower precision than the initial numerical format; evaluating a metric based on the histogram of tensor elements and the target numerical format, the metric indicating a degree of accuracy of a representation of the network tensor in the target numerical format; and based on the evaluated metric, converting the plurality of tensor elements from the initial numerical format to the target numerical format.

Abstract: A computer-implemented method of training a multi-layer neural network comprising a set of network weights, comprising: processing the training data in respective forward and backward passes through multiple layers, the forward pass comprising computing a set of activations in dependence on the network weights and training data, and the backward pass comprising: computing gradients of a pre-determined loss function with respect to the network weights and/or activations, wherein an adjustment parameter is applied to at least a subset of values in the neural network, the values comprising at least one of: the network weights, the activations, the gradients with respect to activations and the gradients with respect to weights; updating the network weights in dependence on the computed gradients; computing a proportion of the subset of values falling above a predefined threshold; and updating the adjustment parameter in dependence on the computed proportion.

Abstract: A computer-implemented method comprising: processing data in a neural network to compute a network tensor comprising a plurality of tensor elements represented in an initial numerical format; computing a histogram of tensor elements; selecting a target numerical format, the target numerical format having a lower precision than the initial numerical format; evaluating a metric based on the histogram of tensor elements and the target numerical format, the metric indicating a degree of accuracy of a representation of the network tensor in the target numerical format; and based on the evaluated metric, converting the plurality of tensor elements from the initial numerical format to the target numerical format.