Introduced a decade ago, reservoir computing is an efficient approach for signal processing. State of the art capabilities have already been demonstrated with both computer simulations and physical implementations. If photonic reservoir...
moreIntroduced a decade ago, reservoir computing is an efficient approach for signal processing. State of the art capabilities have already been demonstrated with both computer simulations and physical implementations. If photonic reservoir computing appears to be promising a solution for ultrafast nontrivial computing, all the implementations presented up to now require digital pre or post processing, which prevents them from exploiting their full potential, in particular in terms of processing speed. We address here the possibility to get rid simultaneously of both digital pre and post processing. The standalone fully analogue reservoir computer resulting from our endeavour is compared to previous experiments and only exhibits rather limited degradation of performances. Our experiment constitutes a proof of concept for standalone physical reservoir computers. Reservoir computing is a bio-inspired approach for processing time dependent information 1-5. A reservoir computer can be decomposed into three parts, see Fig. 1. The "input layer" couples the input signal into a non-linear dynamical system that constitutes the "reservoir layer". The internal variables of the dynamical system, also called "reservoir states", provide a nonlinear mapping of the input into a high dimensional space. Finally the time-dependent output of the reservoir is computed in the "output layer" as a linear combination of the internal variables. The readout weights used to compute this linear combination are optimized so as to minimize the mean square error between the target and the output signal, leading to a simple and easy training process. On the other hand, the values of the internal coupling weights within the input layer and within the reservoir layer are not critical, and can be chosen at random up to some global parameters that are tuned to get the best performance. One of the key advantages of reservoir computers is that, because only the output layer is trained, training algorithms are efficient and rapidly converge to the global optimum. This simplicity enables reservoir computers to solve a large range of complex tasks on time dependent signals, such as speech recognition 6 , nonlinear channel equalization 3,7,8 , detection of epileptic seizures 9 , robot control 10 , time series prediction 1,3 , financial forecasting, handwriting recognition, etc… , often with state of the art performance. We refer to 11-13 for recent reviews. This simplicity and flexibility has also allowed for a breakthrough in analogue information processing, and in particular in optical information processing. The experimental implementations 14-30 of reservoir computing (most of them optical) often report error rates comparable to the best digital algorithms. Most of these experiments, and in particular those that have been able to tackle the most complex tasks, are based on an architecture, introduced experimentally in 15 (see also the earlier report 31 and the theoretical proposal 32,33), consisting of a single nonlinear node and a delay line in which the reservoir states are time multiplexed. These experimental demonstrations are further complemented by extensive studies in simulation of alternative or improved optical implementations 34-41. Despite this intensive research, the potential of reservoir computing in terms of processing easiness and speed has not yet been fully considered. In particular, all previous experiments required either digital pre-processing of the inputs, or digital post-processing of the outputs, or both (i.e. at least either the input layer or the output layer were digitally implemented). This is indeed a major limitation if one intends to use physical reservoir computers as versatile and efficient standalone solutions. Moreover, besides the advantages of speed and versatility, a fully analogue device would allow for the feedback of the output of the reservoir into the reservoir itself, enabling new training techniques 42 as well as the exploitation of reservoir computers to new kinds of tasks, such as pattern generation 3,43. Note that some steps towards a fully analogue reservoir have already been taken. In our unpublished manuscript 44 we showed how to implement an analogue input layer. In fact an analogue input layer is comparatively simpler to implement, as it consists of multiplying the input signal with random weights. The exact values of these