On Computational Power and the Order-Chaos Phase Transition in Reservoir Computing

Randomly connected recurrent neural circuits have proven t o be very powerful models for online computations when a trained memoryless re adout function is appended. Such Reservoir Computing (RC) systems are commonly used in two flavors: with analog or binary (spiking) neurons in the recur rent circuits. Previous work showed a fundamental difference between these two incarnations of the RC idea. The performance of a RC system built from binary neuron s seems to depend strongly on the network connectivity structure. In network s of analog neurons such dependency has not been observed. In this article we investigate this apparent dichotomy in terms of the in-degree of the circuit nodes. Our analyses based amongst others on the Lyapunov exponent reveal that the phase transition between ordered and chaotic network behavior of binary circuits qua litatively differs from the one in analog circuits. This explains the observed decre ased computational performance of binary circuits of high node in-degree. Furt hermore, a novel mean-field predictor for computational performance is intr oduced and shown to accurately predict the numerically obtained results.