1. A method for processing an input through each of a plurality of layers of a neural network to generate an output, wherein each of the plurality of layers of the neural network comprises a respective plurality of nodes, the method comprising, for a particular layer of the plurality of layers: receiving, by a classification system, an activation vector as input for the particular layer; computing a hash code for at least a portion of the activation vector; determining, using a hash table that maps hash values to nodes in the particular layer, one or more most similar hash values in the hash table to the hash code of the portion of the activation vector; selecting one or more nodes in the particular layer that correspond to the one or more most similar hash values, and processing the activation vector using the selected nodes to generate an output for the particular layer.