Delay-based Reservoir Computing: a meeting point for nonlinear dynamics, signal theory, and brain-inspired computing

Nonlinear delay dynamics have attracted lots of interest from their autonomous operation, being capable for various, complex and beautiful behaviors, from period doubling cascade to high dimensional chaos among others. They were also recognized to be relevant models for many practical situations, from physiology to optics through mechanics. In a more applied perspective as for example in photonic, they were used to develop novel encryption schemes that are hiding bit streams into chaotic waveform, decryption being achieved after chaos synchronization ; One also used their extremely long temporal memory provided by large delay to dramatically decrease the phase diffusion constant in microwave oscillators, thus providing high performance (ultra-low phase noise) microwave optoelectronic oscillators for Radar applications. More recently the high dimensional phase space of delay systems and their known analogy with spatio-temporal dynamics, have been used as a technologically feasible and efficient way to emulate a network of neurons, through which novel brain-inspired computing (Reservoir Computing) concepts can be implemented.

In this contribution, we will particularly emphasize on how nonlinear delay dynamics, moreover photonic ones, can be regarded as a kind of recurrent neural network with which spatio-temporal information processing is fully expanded in the time domain through basic signal theory principles. We will show how this description can be used in programming physically classification tasks performed with the bandwidth of Telecom devices, thus reaching record speed up to 1 million words recognized per second with a dedicated photonic hardware.