Response Theory of Spiking Neural Networks

The Feynman machine is a unique model expressing spiking-timing-dependent neural interactions through path integrals. It provides the capability to predict neural firing statistics very precisely. If time-ordered neural interactions are to be represented more properly, however, the classical form of the model needs to be improved. We here introduce how to describe neural interactions by adopting the second quantization formalism; this is requisite for expressing adequately the firing states deviating from a reference state and for calculating firing statistics through a perturbation method. The formulation is also helpful in picking out the neural firings with causal relationships and in predicting activations of a neural network in response to a given external input. This capability is essential for describing the function of a neural network based on the relationship between the input and the output firing patterns.