Synthesis of neural networks for spatio-temporal spike pattern recognition and processing

The advent of large scale neural computational platforms has highlighted the lack of algorithms for synthesis of neural structures to perform predefined cognitive tasks. The Neural Engineering Framework offers one such synthesis, but it is most effective for a spike rate representation of neural information, and it requires a large number of neurons to implement simple functions. We describe a neural network synthesis method that generates synaptic connectivity for neurons which process time-encoded neural signals, and which makes very sparse use of neurons. The method allows the user to specify, arbitrarily, neuronal characteristics such as axonal and dendritic delays, and synaptic transfer functions, and then solves for the optimal input-output relationship using computed dendritic weights. The method may be used for batch or online learning and has an extremely fast optimization process. We demonstrate its use in generating a network to recognize speech which is sparsely encoded as spike times.

A First-Order Non-Homogeneous Markov Model for the Response of Spiking Neurons Stimulated by Small Phase-Continuous Signals

We present a first-order non-homogeneous Markov model for the interspike-interval density of a continuously stimulated spiking neuron. The model allows the conditional interspike-interval density and the stationary interspike-interval density to be expressed as products of two separate functions, one of which describes only the neuron characteristics, and the other of which describes only the signal characteristics. This allows the use of this model to predict the response when the underlying neuron model is not known or well determined. The approximation shows particularly clearly that signal autocorrelations and cross-correlations arise as natural features of the interspike-interval density, and are particularly clear for small signals and moderate noise. We show that this model simplifies the design of spiking neuron cross-correlation systems, and describe a four-neuron mutual inhibition network that generates a cross-correlation output for two input signals.