Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Real-time computation at the edge of chaos in recurrent neural networks
Neural Computation
On the computational power of circuits of spiking neurons
Journal of Computer and System Sciences
Analysis and design of echo state networks
Neural Computation
The introduction of time-scales in reservoir computing, applied to isolated digits recognition
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
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Reservoir Computing is a novel technique which employs recurrent neural networks while circumventing difficult training algorithms. A very recent trend in Reservoir Computing is the use of real physical dynamical systems as implementation platforms, rather than the customary digital emulations. Physical systems operate in continuous time, creating a fundamental difference with the classic discrete time definitions of Reservoir Computing. The specific goal of this paper is to study the memory properties of such systems, where we will limit ourselves to linear dynamics. We develop an analytical model which allows the calculation of the memory function for continuous time linear dynamical systems, which can be considered as networks of linear leaky integrator neurons. We then use this model to research memory properties for different types of reservoir. We start with random connection matrices with a shifted eigenvalue spectrum, which perform very poorly. Next, we transform two specific reservoir types, which are known to give good performance in discrete time, to the continuous time domain. Reservoirs based on uniform spreading of connection matrix eigenvalues on the unit disk in discrete time give much better memory properties than reservoirs with random connection matrices, where reservoirs based on orthogonal connection matrices in discrete time are very robust against noise and their memory properties can be tuned. The overall results found in this work yield important insights into how to design networks for continuous time.