We introduce a novel approach for a complete functional identification of biophysical spike-processing neural circuits. The circuits considered accept multidimensional spike trains as their input and comprise a multitude of temporal receptive fields and conductance-based models of action potential generation. Each temporal receptive field describes the spatiotemporal contribution of all synapses between any two neurons and incorporates the (passive) processing carried out by the dendritic tree. The aggregate dendritic current produced by a multitude of temporal receptive fields is encoded into a sequence of action potentials by a spike generator modeled as a nonlinear dynamical system. Our approach builds on the observation that during any experiment, an entire neural circuit, including its receptive fields and biophysical spike generators, is projected onto the space of stimuli used to identify the circuit. Employing the reproducing kernel Hilbert space (RKHS) of trigonometric polynomials to describe input stimuli, we quantitatively describe the relationship between underlying circuit parameters and their projections. We also derive experimental conditions under which these projections converge to the true parameters. In doing so, we achieve the mathematical tractability needed to characterize the biophysical spike generator and identify the multitude of receptive fields. The algorithms obviate the need to repeat experiments in order to compute the neurons' rate of response, rendering our methodology of interest to both experimental and theoretical neuroscientists.

We investigate a spiking neuron model of multisensory integration. Multiple stimuli from different sensory modalities are encoded by a single neural circuit comprised of a multisensory bank of receptive fields in cascade with a population of biophysical spike generators. We demonstrate that stimuli of different dimensions can be faithfully multiplexed and encoded in the spike domain and derive tractable algorithms for decoding each stimulus from the common pool of spikes. We also show that the identification of multisensory processing in a single neuron is dual to the recovery of stimuli encoded with a population of multisensory neurons, and prove that only a projection of the circuit onto input stimuli can be identified. We provide an example of multisensory integration using natural audio and video and discuss the performance of the proposed decoding and identification algorithms.

In system identification both the input and the output of a system are available to an observer and an algorithm is sought to identify parameters of a hypothesized model of that system. Here we present a novel formal methodology for identifying dendritic processing in a neural circuit consisting of a linear dendritic processing filter in cascade with a spiking neuron model. The input to the circuit is an analog signal that belongs to the space of bandlimited functions. The output is a time sequence associated with the spike train. We derive an algorithm for identification of the dendritic processing filter and reconstruct its kernel with arbitrary precision.