Abstract: Provided is multi-layer neural network technique that includes: calculating, from an input and using a first one or more layers of a plurality of layers of a neural network, a first intermediate output; reducing a size of one or more dimensions of the first intermediate output; calculating, from the first intermediate output and using a second one or more layers of the neural network, a second intermediate output (the second one or more layers including one or more ultra-low precision layers); reducing a size of one or more dimensions of the second intermediate output; combining a plurality of reduced intermediate outputs (including the reduced first intermediate output and the reduced second intermediate output) to derive a combined intermediate output; and calculating, using the combined intermediate output and one or more higher-precision layers of the plurality of layers, a neural network output.