  "Sparse" neural networks, in which relatively few neurons or connections are
active, are common in both machine learning and neuroscience. Whereas in
machine learning, "sparsity" is related to a penalty term that leads to some
connecting weights becoming small or zero, in biological brains, sparsity is
often created when high spiking thresholds prevent neuronal activity. Here we
introduce sparsity into a reservoir computing network via neuron-specific
learnable thresholds of activity, allowing neurons with low thresholds to
contribute to decision-making but suppressing information from neurons with
high thresholds. This approach, which we term "SpaRCe", optimises the sparsity
level of the reservoir without affecting the reservoir dynamics. The read-out
weights and the thresholds are learned by an 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 on classification problems and find that threshold learning improves
performance compared to standard reservoir computing. SpaRCe alleviates the
problem of catastrophic forgetting, a problem most evident in standard echo
state networks and recurrent neural networks in general, due to increasing the
number of task-specialised neurons that are included in the network decisions.
