Channel identification machines

Massively parallel neural circuits for stereoscopic color vision: encoding, decoding and identification

Past work demonstrated how monochromatic visual stimuli could be faithfully encoded and decoded under Nyquist-type rate conditions. Color visual stimuli were then traditionally encoded and decoded in multiple separate monochromatic channels. The brain, however, appears to mix information about color channels at the earliest stages of the visual system, including the retina itself. If information about color is mixed and encoded by a common pool of neurons, how can colors be demixed and perceived? We present Color Video Time Encoding Machines (Color Video TEMs) for encoding color visual stimuli that take into account a variety of color representations within a single neural circuit. We then derive a Color Video Time Decoding Machine (Color Video TDM) algorithm for color demixing and reconstruction of color visual scenes from spikes produced by a population of visual neurons. In addition, we formulate Color Video Channel Identification Machines (Color Video CIMs) for functionally identifying color visual processing performed by a spiking neural circuit. Furthermore, we derive a duality between TDMs and CIMs that unifies the two and leads to a general theory of neural information representation for stereoscopic color vision. We provide examples demonstrating that a massively parallel color visual neural circuit can be first identified with arbitrary precision and its spike trains can be subsequently used to reconstruct the encoded stimuli. We argue that evaluation of the functional identification methodology can be effectively and intuitively performed in the stimulus space. In this space, a signal reconstructed from spike trains generated by the identified neural circuit can be compared to the original stimulus.

Channel identification machines for multidimensional receptive fields

We present algorithms for identifying multidimensional receptive fields directly from spike trains produced by biophysically-grounded neuron models. We demonstrate that only the projection of a receptive field onto the input stimulus space may be perfectly identified and derive conditions under which this identification is possible. We also provide detailed examples of identification of neural circuits incorporating spatiotemporal and spectrotemporal receptive fields.

Volterra dendritic stimulus processors and biophysical spike generators with intrinsic noise sources

We consider a class of neural circuit models with internal noise sources arising in sensory systems. The basic neuron model in these circuits consists of a dendritic stimulus processor (DSP) cascaded with a biophysical spike generator (BSG). The dendritic stimulus processor is modeled as a set of nonlinear operators that are assumed to have a Volterra series representation. Biophysical point neuron models, such as the Hodgkin-Huxley neuron, are used to model the spike generator. We address the question of how intrinsic noise sources affect the precision in encoding and decoding of sensory stimuli and the functional identification of its sensory circuits. We investigate two intrinsic noise sources arising (i) in the active dendritic trees underlying the DSPs, and (ii) in the ion channels of the BSGs. Noise in dendritic stimulus processing arises from a combined effect of variability in synaptic transmission and dendritic interactions. Channel noise arises in the BSGs due to the fluctuation of the number of the active ion channels. Using a stochastic differential equations formalism we show that encoding with a neuron model consisting of a nonlinear DSP cascaded with a BSG with intrinsic noise sources can be treated as generalized sampling with noisy measurements. For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding. Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given. We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.

Spiking neural circuits with dendritic stimulus processors : encoding, decoding, and identification in reproducing kernel Hilbert spaces

We present a multi-input multi-output neural circuit architecture for nonlinear processing and encoding of stimuli in the spike domain. In this architecture a bank of dendritic stimulus processors implements nonlinear transformations of multiple temporal or spatio-temporal signals such as spike trains or auditory and visual stimuli in the analog domain. Dendritic stimulus processors may act on both individual stimuli and on groups of stimuli, thereby executing complex computations that arise as a result of interactions between concurrently received signals. The results of the analog-domain computations are then encoded into a multi-dimensional spike train by a population of spiking neurons modeled as nonlinear dynamical systems. We investigate general conditions under which such circuits faithfully represent stimuli and demonstrate algorithms for (i) stimulus recovery, or decoding, and (ii) identification of dendritic stimulus processors from the observed spikes. Taken together, our results demonstrate a fundamental duality between the identification of the dendritic stimulus processor of a single neuron and the decoding of stimuli encoded by a population of neurons with a bank of dendritic stimulus processors. This duality result enabled us to derive lower bounds on the number of experiments to be performed and the total number of spikes that need to be recorded for identifying a neural circuit.

Functional identification of spike-processing neural circuits

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.

Computational identification of receptive fields

Natural stimuli elicit robust responses of neurons throughout sensory pathways, and therefore their use provides unique opportunities for understanding sensory coding. This review describes statistical methods that can be used to characterize neural feature selectivity, focusing on the case of natural stimuli. First, we discuss how such classic methods as reverse correlation/spike-triggered average and spike-triggered covariance can be generalized for use with natural stimuli to find the multiple relevant stimulus features that affect the responses of a given neuron. Second, ways to characterize neural feature selectivity while assuming that the neural responses exhibit a certain type of invariance, such as position invariance for visual neurons, are discussed. Finally, we discuss methods that do not require one to make an assumption of invariance and instead can determine the type of invariance by analyzing relationships between the multiple stimulus features that affect the neural responses.