Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for implementing brain emulation neural networks using compressed matrix representations. One of the methods includes obtaining a network input; and processing the network input using a neural network to generate a network output, comprising: processing the network input using an input subnetwork of the neural network to generate an embedding of the network input; and processing the embedding of the network input using a brain emulation subnetwork of the neural network, wherein the brain emulation subnetwork has a brain emulation neural network architecture that represents synaptic connectivity between a plurality of biological neurons in a brain of a biological organism, the processing comprising: obtaining a compressed matrix representation of a sparse matrix of brain emulation parameters; and applying the compressed matrix representation to the embedding of the network input to generate a brain emulation subnetwork output.