Sparse coding has been posited as an efficient information processing strategy employed by sensory systems, particularly visual cortex. Substantial theoretical and experimental work has focused on the issue of sparse encoding, namely how the early visual system maps the scene into a sparse representation. In this paper we investigate the complementary issue of sparse decoding, for example given activity generated by a realistic mapping of the visual scene to neuronal spike trains, how do downstream neurons best utilize this representation to generate a "decision." Specifically we consider both sparse (L1-regularized) and non-sparse (L2 regularized) linear decoding for mapping the neural dynamics of a large-scale spiking neuron model of primary visual cortex (V1) to a two alternative forced choice (2-AFC) perceptual decision. We show that while both sparse and non-sparse linear decoding yield discrimination results quantitatively consistent with human psychophysics, sparse linear decoding is more efficient in terms of the number of selected informative dimension.

Age-related macular degeneration (AMD) is the major cause of blindness in the developed world. Though substantial work has been done to characterize the disease, it is difficult to predict how the state of an individual's retina will ultimately affect their high-level perceptual function. In this paper, we describe an approach that couples retinal imaging with computational neural modeling of early visual processing to generate quantitative predictions of an individual's visual perception. Using a patient population with mild to moderate AMD, we show that we are able to accurately predict subject-specific psychometric performance by decoding simulated neurodynamics that are a function of scotomas derived from an individual's fundus image. On the population level, we find that our approach maps the disease on the retina to a representation that is a substantially better predictor of high-level perceptual performance than traditional clinical metrics such as drusen density and coverage. In summary, our work identifies possible new metrics for evaluating the efficacy of treatments for AMD at the level of the expected changes in high-level visual perception and, in general, typifies how computational neural models can be used as a framework to characterize the perceptual consequences of early visual pathologies.

Drusen, the hallmark lesions of age related macular degeneration (AMD), are biochemically heterogeneous and the identification of their biochemical distribution is key to the understanding of AMD. Yet the challenges are to develop imaging technology and analytics, which respect the physical generation of the hyperspectral signal in the presence of noise, artifacts, and multiple mixed sources while maximally exploiting the full data dimensionality to uncover clinically relevant spectral signatures. This paper reports on the statistical analysis of hyperspectral signatures of drusen and anatomical regions of interest using snapshot hyperspectral imaging and non-negative matrix factorization (NMF). We propose physical meaningful priors as initialization schemes to NMF for finding low-rank decompositions that capture the underlying physiology of drusen and the macular pigment. Preliminary results show that snapshot hyperspectral imaging in combination with NMF is able to detect biochemically meaningful components of drusen and the macular pigment. To our knowledge, this is the first reported demonstration in vivo of the separate absorbance peaks for lutein and zeaxanthin in macular pigment.

Recent empirical evidence supports the hypothesis that invariant visual object recognition might result from non-linear encoding of the visual input followed by linear decoding. This hypothesis has received theoretical support through the development of neural network architectures which are based on a non-linear encoding of the input via recurrent network dynamics followed by a linear decoder. In this paper we consider such an architecture in which the visual input is non-linearly encoded by a biologically realistic spiking model of V1, and mapped to a perceptual decision via a sparse linear decoder. Novel is that we (1) utilize a large-scale conductance based spiking neuron model of V1 which has been well-characterized in terms of classical and extra-classical response properties, and (2) use the model to investigate decoding over a large population of neurons. We compare decoding performance of the model system to human performance by comparing neurometric and psychometric curves.

We investigate using a previously developed spiking neuron model of layer 4 of primary visual cortex (V1) [1] as a recurrent network whose activity is consequently linearly decoded, given a set of complex visual stimuli. Our motivation is based on the following: 1) Linear decoders have proven useful in analyzing a variety of neural signals, including spikes, firing rates, local field potentials, voltage sensitive dye imaging, and scalp EEG, 2) linear decoding of activity generated from highly recurrent, nonlinear networks with fixed connections has been shown to provide universal computational capabilities, with such methods termed liquid state machines (LSM) [2] and echo state networks (ESN) [3], 3) in LSMs or ESNs often little is assumed about the recurrent network architecture. However it is likely that for a given type of stimulus/input, the architecture of a biologically constrained recurrent network is important since it shapes the spatio-temporal correlations across the neuronal population, which can potentially be exploited efficiently by an appropriate decoder.

Two competing phenomological models of extraclassical spatial summation in V1 are the differenceof-Gaussians (DoG) and the ratio-of-Gaussians (RoG) which argue for subtractive or divisive normalization, respectively, as the basis for a variety of extraclassical response properties, such as surround suppression and contrast-dependent receptive field growth. Problematic with these models, however, is that they are somewhat removed from the neurophysiology and thus do not lend themselves to inferring underlying mechanisms. Simulations of an anatomically and physiologically detailed large-scale spiking neuron model, which we have previous developed [1], indicate that the interaction between excitatory and inhibitory cortical conductances may be at the root of the these extraclassical phenomena and that both subtractive and divisive effects of cortical inhibition are involved. Moreover, Anderson et al showed, using intracellular recordings from cat, that cortical conductances are oscillatory [2], with stronger modulation in the inhibitory conductance. Based on these two observations, we developed a

We present a large-scale anatomically constrained spiking neuron model of the lateral geniculate nucleus (LGN), which operates solely with retinal input, relay cells, and interneurons. We show that interneuron inhibition and sparse connectivity between LGN cells could be key factors for explaining a number of observed classical and extraclassical response properties in LGN of monkey and cat. Among them are 1) weak orientation tuning, 2) contrast invariance of spatial frequency tuning in the absence of cortical feedback, 3) extraclassical surround suppression, and 4) orientation tuning of extraclassical surround suppression. The model also makes two surprising predictions: 1) a possible pinwheel-like spatial organization of orientation preference in the parvo layers of monkey LGN, much like what is seen in V1, and 2) a stimulus-induced trend (bias) in the orientation and phase preference of surround suppression, originating from the stimulus discontinuity between center and surround gratings rather than from specific circuitry.

In this paper we analyze a popular divisive normalization model of V1 with respect to the relationship between its underlying coding strategy and the extraclassical physiological responses of its constituent modeled neurons. Specifically we are interested in whether the optimization goal of redundancy reduction naturally leads to reasonable neural responses, including reasonable distributions of responses. The model is trained on an ensemble of natural images and tested using sinusoidal drifting gratings, with metrics such as suppression index and contrast dependent receptive field growth compared to the objective function values for a sample of neurons. We find that even though the divisive normalization model can produce "typical" neurons that agree with some neurophysiology data, distributions across samples do not agree with experimental data. Our results suggest that redundancy reduction itself is not necessarily causal of the observed extraclassical receptive field phenomena, and that additional optimization dimensions and/or biological constraints must be considered

Based on a large-scale neural network model of striate cortex (V1), we present a simulation study of extra- and intracellular response modulations for drifting and contrast reversal grating stimuli. Specifically, we study the dependency of these modulations on the neural circuitry. We find that the frequently used ratio of the first harmonic to the mean response to classify simple and complex cells is highly insensitive to circuitry. Limited experimental sample size for the distribution of this measure makes it unsuitable for distinguishing whether the dichotomy of simple and complex cells originates from distinct LGN axon connectivity and/or local circuitry in V1. We show that a possible useful measure in this respect is the ratio of the intracellular second- to first-harmonic response for contrast reversal gratings. This measure is highly sensitive to neural circuitry and its distribution can be sampled with sufficient accuracy from a limited amount of experimental data. Further, the distribution of this measure is qualitatively similar to that of the subfield correlation coefficient, although it is more robust and easier to obtain experimentally.

Using a large scale model of macaque V1, we have shown (Wielaard & Sajda 2003, 2005) how only local short-range (<0.5 mm) connections within V1 can mediate surround suppression and account for a large fraction of the magnitude of suppression seen experimentally. In our model surround suppression arises from one of three mechanisms: (A) an increase in cortical inhibition, (B) a decrease in cortical excitation, or (C) both of these simultaneously. It is known that LGN neurons exhibit both classical and extraclassical surround suppression, with classical surround suppression observed at lower spatial frequencies. This leaves open the question of whether the unexplained fraction of suppression seen in our model could be inherited from the LGN or instead requires considering long-range lateral connections and/or extrastriate feedback. Using our model, we consider the effect of classical LGN surround suppression on suppression in V1 cortical neurons, in particular by measuring the distribution of the suppression index at spatial frequencies that are a quarter of those typically used to optimally drive cortical neurons. We find that at these lower spatial frequencies, nearly all of the classical surround suppression of LGN cells is transferred to V1 cells, either via direct LGN input into the cell and/or suppression of recurrent cortico-cortical excitation. We also see that at these low spatial frequencies, the prevalence of the cortical mechanisms for surround suppression is shifted in favor of mechanisms B and C, which rely on the reduction of excitation. This shift occurs at the expense of mechanism A, which relies on direct inhibition. Our model thus predicts 1) a substantial increase in V1 surround suppression is possible by sufficiently lowering the stimulus spatial frequency and 2) that ultimately the magnitude of surround suppression seen in V1 neurons is explainable by considering only the short-range cortical connections and the LGN input.

Based on a large scale spiking neuron model of the input layers 4Cα and β of macaque, we identify neural mechanisms for the observed contrast dependent receptive field size of V1 cells. We observe a rich variety of mechanisms for the phenomenon and analyze them based on the relative gain of excitatory and inhibitory synaptic inputs. We observe an average growth in the spatial extent of excitation and inhibition for low contrast, as predicted from phenomenological models. However, contrary to phenomenological models, our simulation results suggest this is neither sufficient nor necessary to explain the phenomenon.

Using a rectification model and an experimentally measured distribution of the extracellular modulation ratio (F1/F0), we investigate the consistency between extracellular and intracellular modulation metrics for classifying cells in primary visual cortex (V1). We first demonstrate that the shape of the distribution of the intracellular metric χ is sensitive to the specific form of the bimodality observed in F1/F0. When the proper mapping between F1/F0 and χ is applied to the experimentally measured F1/F0 data, χ is weakly bimodal. We then use a two-class mixture model to estimate physiological response parameters given the F1/F0 distribution. We show, once again, that a weak bimodality is present in χ. Finally, using the estimated parameters for the two cell clases, we show that simple and complex cell class assignment in F1/F0 is more-or-less preserved in a heavy-tailed f1/f0 distribution, with complex cells being in the core of the f1/f0 distribution and simple cells in the tail (misclassification error in f1/f0 = 19%). Class assignment in f1/f0 is likewise consistent (misclassification error in F1/F0 = 15%). Our results provide computational support for the conclusion that extracellular and intracellular metrics are relatively consistent measures for classifying cells in V1 as either simple or complex. ∗Department of Biomedical Engineering, Columbia University,New York, NY 10027; (al2082, mgp2101, djw21, ps629)@columbia.edu. This research was supported by the DoD Multidisciplinary University Research Initiative (MURI) program administered by the Office of Naval Research (N00014-01-0625) and NGA grant HM1582-05-C-0008 Consistency of Extracellular and Intracellular Classification of Simple and Complex Cells An Luo, Marios Philiastides, Jim Wielaard and Paul Sajda Department of Biomedical Engineering, Columbia University,New York, NY 10027 (al2082, mgp2101, djw21, ps629)@columbia.edu. Introduction It has been observed that the ratio between the amplitude of the first harmonic of the response to the mean firing rate (F1/F0) when a cell is responding to drifting sinusoidal gratings is bimodally distributed over the V1 population. Furthermore, this bimodality is perceived as evidence for the existence of two discrete classes of cells [1]. Mechler and Ringach [2] however, have proposed that the bimodality of F1/F0 does not necessarily imply the existence of two cell classes. Using a rectification model, they show that a bimodal distribution in F1/F0 can be observed even when the distribution of a parameter χ, closely linked to the intracellular modulation ratio f1/f0, is unimodal. Since f1/f0 , and therefore χ, is more directly linked to the synaptic drive of the neurons, it can be argued that it is likely to be a better metric than F1/F0 for inferring the presence of underlying cell classes. In this paper we investigate the issue of simple and complex cell classification with respect to the consistency of the extracellular and intracellular modulation ratios. Similar to [2], we model neuron responses using a rectification model. Somewhat differently, however, we use the experimentally observed data for F1/F0 reported in [2] to fit model parameters and estimate χ and f1/f0. We first show that the nonlinear mapping from F1/F0 to χ results in a weak bimodal distribution for χ if one uses the experimentally observed F1/F0 distribution. We next use a rectification model, similar to that used in [2], to estimate parameters for both a one class and two class model that best fit the experimentally observed distribution of F1/F0. Finally we use the estimated parameters for the two cell class model to investigate the consistency of simple and complex classification when labeling in F1/F0 and evaluating the class distribution in f1/f0, and vice versa. The rectification model We assume that a neuron’s membrane potential in response to a sinusoidal drifting grating at preferred orientation and spatial frequency consists of a sinusoidal waveform driven at the temporal frequency of the stimulus, with amplitude A, and mean voltage potential Vm. A neuron’s instantaneous firing rate, r(t), is assumed to be proportional to the supra-threshold membrane potential and zero if the membrane potential remains below the threshold, Vt. Eqn. 1&2 summarize this rectification model. v(t) = Vm + A cos(2πft) (1) r(t) = G[v(t) − Vt] (2) In Eqn. 2, G is the gain related to the spike generator. The intracellular modulation ratio f1/f0 is defined as A/(Vm − VI), where VI is the inhibitory reverse potential. The extracellular modulation ratio F1/F0 is given by F0 = 1 2π ∫ 2π 0 r(t)dt and F1 = 1 2π ∫ 2π 0 r(t) cos(2πft)dt. In their paper [2], Mechler and Ringach define an intracellular ratio parameter χ = (Vt − Vm)/A, and prove that F1/F0 is a nonlinear monotonic function of χ, F1/F0 = f(χ) = 

We have developed a large-scale computational model of a 4x4 mm(2) patch of a primary visual cortex (V1) input layer. The model is constructed from basic established anatomical and physiological data. Based on numerical simulations with this model we are able to suggest neural mechanisms for a wide variety of classical response properties of V1, as well as for a number of extraclassical receptive field phenomena. The nature of our model is such that we are able to address stationary as well as dynamical behaviour of V1, both on the single cell level and on a population level of up to about 10(4) cells.

Neural mechanisms of extraclassical receptive field phenomena in V1 are commonly assumed to result from long-range lateral connections and/or extrastriate feedback. We address two such phenomena: surround suppression and contrast dependent receptive field size. We present rigorous computational support for the hypothesis that the phenomena largely result from local short-range (< 0.5 mm) cortical connections and LGN input. Surround suppression in our simulations results from (A) direct cortical inhibition or (B) suppression of recurrent cortical excitation, or (C) action of both these mechanisms simultaneously. Mechanisms B and C are substantially more prevalent than A. We observe an average growth in the range of spatial summation of excitatory and inhibitory synaptic inputs for low contrast. However, we find this is neither sufficient nor necessary to explain contrast dependent receptive field size, which usually involves additional changes in the relative gain of these inputs.