Sparsity in Reservoir Computing Neural Networks

Reservoir Computing (RC) is a well-known strategy for designing Recurrent Neural Networks featured by striking efficiency of training. The crucial aspect of RC is to properly instantiate the hidden recurrent layer that serves as dynamical memory to the system. In this respect, the common recipe is to create a pool of randomly and sparsely connected recurrent neurons. While the aspect of sparsity in the design of RC systems has been debated in the literature, it is nowadays understood mainly as a way to enhance the efficiency of computation, exploiting sparse matrix operations. In this paper, we empirically investigate the role of sparsity in RC network design under the perspective of the richness of the developed temporal representations. We analyze both sparsity in the recurrent connections, and in the connections from the input to the reservoir. Our results point out that sparsity, in particular in input-reservoir connections, has a major role in developing internal temporal representations that have a longer short-term memory of past inputs and a higher dimension.