On the computational power of noisy spiking neurons

W. Maass

Abstract:

It has remained unknown wether one can in principle carry out reliable digital computations with networks of biologically realistic models for neurons. This article presents rigorous constructions for simulating in real-time arbitrary given boolean circuits and finite automata with arbitrarily high reliability by networks of noisy spiking neurons. In addition we show that with the help of "shunting inhibition" even networks of very unreliable spiking neurons can simulate in real-time any McCulloch-Pitts neuron (or "threshold gate"), and therefore any multilayer perceptron (or "threshold circuit") in a reliable manner. These constructions provide a possible explanation for the fact that biological neural systems can carry out quite complex computations within 100 msec. It turns out that the assumption that these constructions require about the shape of EPSP's and the behaviour of the noise are surprisingly weak.

Reference: W. Maass. On the computational power of noisy spiking neurons. In D. Touretzky, M. C. Mozer, and M. E. Hasselmo, editors, Advances in Neural Information Processing Systems, volume 8, pages 211-217. MIT Press (Cambridge), 1996.