Computing using delayed feedback systems: towards photonics

Reservoir computing has recently been introduced as a new paradigm in the field of machine learning. It is based on the dynamical properties of a network of randomly connected nodes or neurons and shows to be very promising to solve complex classification problems in a computationally efficient way. The key idea is that an input generates nonlinearly transient behavior rendering transient reservoir states suitable for linear classification. Our goal is to study up to which extent systems with delay, and especially photonic systems, can be used as reservoirs. Recently an new architecture has been proposed(1), based on a single nonlinear node with delayed feedback. An electronic 1 and an opto-electronic implementation(2, 3) have been demonstrated and both have proven to be very successful in terms of performance. This simple configuration, which replaces an entire network of randomly connected nonlinear nodes with one single hardware node and a delay line, is significantly easier to implement experimentally. It is no longer necessary to construct an entire network of hundreds or even thousands of circuits, each one representing a node. With this approach one node and a delay line suffice to construct a computational unit. In this manuscript, we present a further investigation of the properties of delayed feedback con figurations used as a reservoir. Instead of quantifying the performance as an error obtained for a certain benchmark, we now investigate a task-independent property, the linear memory of the system