Dissecting cascade computational components in spiking neural networks

Finding out the physical structure of neuronal circuits that governs neuronal responses is an important goal for brain research. With fast advances for large-scale recording techniques, identification of a neuronal circuit with multiple neurons and stages or layers becomes possible and highly demanding. Although methods for mapping the connection structure of circuits have been greatly developed in recent years, they are mostly limited to simple scenarios of a few neurons in a pairwise fashion; and dissecting dynamical circuits, particularly mapping out a complete functional circuit that converges to a single neuron, is still a challenging question. Here, we show that a recent method, termed spike-triggered non-negative matrix factorization (STNMF), can address these issues. By simulating different scenarios of spiking neural networks with various connections between neurons and stages, we demonstrate that STNMF is a persuasive method to dissect functional connections within a circuit. Using spiking activities recorded at neurons of the output layer, STNMF can obtain a complete circuit consisting of all cascade computational components of presynaptic neurons, as well as their spiking activities. For simulated simple and complex cells of the primary visual cortex, STNMF allows us to dissect the pathway of visual computation. Taken together, these results suggest that STNMF could provide a useful approach for investigating neuronal systems leveraging recorded functional neuronal activity.

New End-Stopped Complex Cell Model Applicable in Convolutional Neural Networks

This article is dedicated to modeling the end-stopped neuron. This type of neuron gives the maximum response at the end of the line and is used to refine the edge. The article provides an overview of different models of end-stopped neurons. I have proposed a simpler and more accurate model of an end-stopped neuron based on the use of Gabor filters in antiphase. For this purpose, the models of simple and complex cells whose output is used in the proposed model are also described. Simple cells are based on the use of a Gabor filter, the parameters of which are also described in this article. The proposed model has shown its effectiveness.

Simultaneous development and periodic clustering of simple and complex cells in visual cortex

Neurons in the primary visual cortex (V1) are often classified as simple or complex cells, but it is debated whether they are discrete hierarchical classes of neurons developing sequentially, or if they represent a continuum of variation within a single class of cells developing simultaneously. Herein, we show that simple and complex cells may arise simultaneously from the universal process of retinal development. From analysis of the cortical receptive fields in cats, we show evidence that simple and complex cells originate from the periodic variation of ON-OFF segregation in the feedforward projection of retinal mosaics, by which they organize into periodic clusters in V1. Our key prediction that clusters of simple and complex cells correlate topographically with orientation maps was confirmed by data in cats. Our results suggest that simple and complex cells are not two distinct neural populations but arise from common retinal afferents, simultaneous with orientation tuning.HighlightsSimple and complex cells arise simultaneously from retinal afferents.Simple/complex cells are organized into periodic clusters across visual cortex.Simple/complex clusters are topographically correlated with orientation maps.Development of clustered cells in V1 is explained by the Paik-Ringach model.

Quantum-like signal-tuned approach to V1 modeling

Signal-tuned Gabor functions — Gaussian-modulated sinusoids whose parameters are determined by a spatial or spectral “tuning signal” — have previously been shown to provide a plausible model for the stimulus-dependent receptive fields and responses of the simple and complex cells of the primary visual cortex (V1). The signal-tuned responses obey Schrödinger equations, which has led to the proposal of a quantum-like model for V1 cells: by considering the squared magnitude of a particular signal-tuned wave function as a probability density, one arrives at a Poisson spiking process which appears consistent with the neurophysiological findings. Here, by incorporating Hermite-polynomial factors to the signal-tuned Gabor functions, we obtain a generalized quantum-like signal-tuned model for which further relevant properties are demonstrated, such as receptive-field coding of the stimulus and its derivatives, saturating spatial summation curves and half-wave rectification of the simple cell responses. Although only a one-dimensional approach is considered here, such properties will carry over to a two-dimensional model, in which case, as our preliminary analysis indicates, end-stopping — another important feature of cortical cells — can also be accommodated.

The divisive normalization model of V1 neurons: a comprehensive comparison of physiological data and model predictions

The physiological responses of simple and complex cells in the primary visual cortex (V1) have been studied extensively and modeled at different levels. At the functional level, the divisive normalization model (DNM; Heeger DJ. Vis Neurosci 9: 181–197, 1992) has accounted for a wide range of single-cell recordings in terms of a combination of linear filtering, nonlinear rectification, and divisive normalization. We propose standardizing the formulation of the DNM and implementing it in software that takes static grayscale images as inputs and produces firing rate responses as outputs. We also review a comprehensive suite of 30 empirical phenomena and report a series of simulation experiments that qualitatively replicate dozens of key experiments with a standard parameter set consistent with physiological measurements. This systematic approach identifies novel falsifiable predictions of the DNM. We show how the model simultaneously satisfies the conflicting desiderata of flexibility and falsifiability. Our key idea is that, while adjustable parameters are needed to accommodate the diversity across neurons, they must be fixed for a given individual neuron. This requirement introduces falsifiable constraints when this single neuron is probed with multiple stimuli. We also present mathematical analyses and simulation experiments that explicate some of these constraints.