Reservoir Computing Based on Dynamics of Pseudo-Billiard System in Hypercube

Reservoir computing (RC) is a framework for constructing recurrent neural networks with simple training rule and sparsely and randomly connected nonlinear units. The network (called reservoir) generates complex motion that can be used for many tasks including time series generation and prediction. We construct a reservoir based on the dynamics of the pseudo-billiard system that produce complex motion in a high-dimensional hypercube. In particular, we use the chaotic Boltzmann machine (CBM) whose units exhibit chaotic behavior in the hypercube. The units interact with each other in a time-domain manner through its binary state, and thus an efficient hardware implementation of the system is expected. In order to utilize the CBM as the reservoir, it is necessary to control its chaotic behavior for ensuring the echo state property of RC and establish encoding and decoding for input and output signal. For this purpose, we introduce a reference clock and analyze effects and properties of the reference input. We evaluate the proposed model on the time series generation tasks and show that the model works properly on a broad range of parameter values. Our approach presents a novel mechanism for time-domain information processing and a fundamental technology for a brain like artificial intelligence system.