End-to-end data format selection for hardware implementation of deep neural network

Selecting optimal fixed point number formats for representing weights and optimal formats for representing values input to and/or output from layers of a deep neural network, DNN, which take into account the impact of the fixed point number formats for that element, i.e. weight/input/output, on a particular layer in the context of the DNN. The methods comprise selecting the fixed-point number format(s) used to represent value sets for a layer one value set at a time before moving on to the next layer and doing the same for a layer at a time in a predetermined sequence. Layers are preceded in the sequence of their interdependency during the operation of the DNN. The fixed-point number format(s) for each layer are selected based on the error in the output of the DNN associated with the fixed-point number formats. Once the fixed point number format(s) for a layer have been selected any calculation of the error in the output of the DNN for a subsequent layer in the sequence is based on that layer being configured to use the selected fixed point number formats.