SpaRCe: Sparse reservoir computing

"Sparse" neural networks, in which relatively few neurons or connections are active, are common in both machine learning and neuroscience. Whereas in machine learning, "sparseness" is related to a penalty term which effectively leads to some connecting weights becoming small or zero, in biological brains, sparseness is often created when high spiking thresholds prevent neuronal activity. Inspired by neuroscience, here we introduce sparseness into a reservoir computing network via neuron-specific learnable thresholds of activity, allowing neurons with low thresholds to give output but silencing outputs from neurons with high thresholds. This approach, which we term "SpaRCe", optimises the sparseness level of the reservoir and applies the threshold mechanism to the information received by the read-out weights. Both the read-out weights and the thresholds are learned by a standard on-line gradient rule that minimises an error function on the outputs of the network. Threshold learning occurs by the balance of two opposing forces: reducing inter-neuronal correlations in the reservoir by deactivating redundant neurons, while increasing the activity of neurons participating in correct decisions. We test SpaRCe in a set of classification problems and find that introducing threshold learning improves performance compared to standard reservoir computing networks.