Exploiting Signal Propagation Delays to match Task Memory Requirements in Reservoir Computing

Recurrent neural networks (RNNs) transmit information over time through recurrent connections. In contrast, biological neural networks use many other temporal processing mechanisms. One of these mechanisms is the inter-neuron delays caused by varying axon properties. Recently, this feature was implemented in echo state networks (ESNs), a type of RNN, by assigning spatial locations to neurons and introducing distance-dependent inter-neuron delays. These delays were shown to significantly improve ESN task performance. However, thus far it is still unclear why distance-based delay networks (DDNs) perform bettern than ESNs. In this paper, we show that by optimizing inter-node delays, the memory capacity of the network matches the memory requirements of the task. As such, networks concentrate their memory capabilities to the points in the past which contain the most information for the task at hand. Moreover, we show that DDNs have more total linear memory capacity, with the same amount of non-linear processing power.