Cooperative and competitive interactions facilitate stereo computations in macaque primary visual cortex

Surface slant impairs disparity discontinuity discrimination

Binocular disparity signals are highly informative about the three-dimensional structure of visual scenes, including aiding the detection of depth discontinuities between surfaces. Here, we examine factors affecting sensitivity to such surface discontinuities. Participants were presented with random dot stereograms depicting two planar surfaces slanted in opposite directions and were asked to judge the sign of the depth discontinuity created where those surfaces met. Although the judgement was focussed on the adjacent edges, the precision of depth discontinuity discrimination depended upon the slant of the two surfaces: increasing surface slants to ±60° increased discontinuity discrimination thresholds by, on average, a factor of 5. Control experiments examining discontinuity discrimination across surfaces with identical slants showed either biases in discontinuity judgements or reduced threshold elevation. These results suggest that sensitivity to depth discontinuities is affected by processing limitations in both local absolute disparity measurement mechanisms and mechanisms selective for disparity differences. As further evidence in support of this conclusion, we show that our results are well-described by a model of discontinuity discrimination based on the encoding of local differences in relative disparity.

Adaptive Tuning Curve Widths Improve Sample Efficient Learning

Natural brains perform miraculously well in learning new tasks from a small number of samples, whereas sample efficient learning is still a major open problem in the field of machine learning. Here, we raise the question, how the neural coding scheme affects sample efficiency, and make first progress on this question by proposing and analyzing a learning algorithm that uses a simple reinforce-type plasticity mechanism and does not require any gradients to learn low dimensional mappings. It harnesses three bio-plausible mechanisms, namely, population codes with bell shaped tuning curves, continous attractor mechanisms and probabilistic synapses, to achieve sample efficient learning. We show both theoretically and by simulations that population codes with broadly tuned neurons lead to high sample efficiency, whereas codes with sharply tuned neurons account for high final precision. Moreover, a dynamic adaptation of the tuning width during learning gives rise to both, high sample efficiency and high final precision. We prove a sample efficiency guarantee for our algorithm that lies within a logarithmic factor from the information theoretical optimum. Our simulations show that for low dimensional mappings, our learning algorithm achieves comparable sample efficiency to multi-layer perceptrons trained by gradient descent, although it does not use any gradients. Furthermore, it achieves competitive sample efficiency in low dimensional reinforcement learning tasks. From a machine learning perspective, these findings may inspire novel approaches to improve sample efficiency. From a neuroscience perspective, these findings suggest sample efficiency as a yet unstudied functional role of adaptive tuning curve width.

Adjusted regularization of cortical covariance

It is now common to record dozens to hundreds or more neurons simultaneously, and to ask how the network activity changes across experimental conditions. A natural framework for addressing questions of functional connectivity is to apply Gaussian graphical modeling to neural data, where each edge in the graph corresponds to a non-zero partial correlation between neurons. Because the number of possible edges is large, one strategy for estimating the graph has been to apply methods that aim to identify large sparse effects using an [Formula: see text] penalty. However, the partial correlations found in neural spike count data are neither large nor sparse, so techniques that perform well in sparse settings will typically perform poorly in the context of neural spike count data. Fortunately, the correlated firing for any pair of cortical neurons depends strongly on both their distance apart and the features for which they are tuned. We introduce a method that takes advantage of these known, strong effects by allowing the penalty to depend on them: thus, for example, the connection between pairs of neurons that are close together will be penalized less than pairs that are far apart. We show through simulations that this physiologically-motivated procedure performs substantially better than off-the-shelf generic tools, and we illustrate by applying the methodology to populations of neurons recorded with multielectrode arrays implanted in macaque visual cortex areas V1 and V4.

Dynamic mechanisms of visually guided 3D motion tracking

The continuous perception of motion-through-depth is critical for both navigation and interacting with objects in a dynamic three-dimensional (3D) world. Here we used 3D tracking to simultaneously assess the perception of motion in all directions, facilitating comparisons of responses to motion-through-depth to frontoparallel motion. Observers manually tracked a stereoscopic target as it moved in a 3D Brownian random walk. We found that continuous tracking of motion-through-depth was selectively impaired, showing different spatiotemporal properties compared with frontoparallel motion tracking. Two separate factors were found to contribute to this selective impairment. The first is the geometric constraint that motion-through-depth yields much smaller retinal projections than frontoparallel motion, given the same object speed in the 3D environment. The second factor is the sluggish nature of disparity processing, which is present even for frontoparallel motion tracking of a disparity-defined stimulus. Thus, despite the ecological importance of reacting to approaching objects, both the geometry of 3D vision and the nature of disparity processing result in considerable impairments for tracking motion-through-depth using binocular cues.NEW & NOTEWORTHY We characterize motion perception continuously in all directions using an ecologically relevant, manual target tracking paradigm we recently developed. This approach reveals a selective impairment to the perception of motion-through-depth. Geometric considerations demonstrate that this impairment is not consistent with previously observed spatial deficits (e.g., stereomotion suppression). However, results from an examination of disparity processing are consistent with the longer latencies observed in discrete, trial-based measurements of the perception of motion-through-depth.

Population activity structure of excitatory and inhibitory neurons

Many studies use population analysis approaches, such as dimensionality reduction, to characterize the activity of large groups of neurons. To date, these methods have treated each neuron equally, without taking into account whether neurons are excitatory or inhibitory. We studied population activity structure as a function of neuron type by applying factor analysis to spontaneous activity from spiking networks with balanced excitation and inhibition. Throughout the study, we characterized population activity structure by measuring its dimensionality and the percentage of overall activity variance that is shared among neurons. First, by sampling only excitatory or only inhibitory neurons, we found that the activity structures of these two populations in balanced networks are measurably different. We also found that the population activity structure is dependent on the ratio of excitatory to inhibitory neurons sampled. Finally we classified neurons from extracellular recordings in the primary visual cortex of anesthetized macaques as putative excitatory or inhibitory using waveform classification, and found similarities with the neuron type-specific population activity structure of a balanced network with excitatory clustering. These results imply that knowledge of neuron type is important, and allows for stronger statistical tests, when interpreting population activity structure.

Evidence of Stereoscopic Surface Disambiguation in the Responses of V1 Neurons

For the important task of binocular depth perception from complex natural-image stimuli, the neurophysiological basis for disambiguating multiple matches between the eyes across similar features has remained a long-standing problem. Recurrent interactions among binocular disparity-tuned neurons in the primary visual cortex (V1) could play a role in stereoscopic computations by altering responses to favor the most likely depth interpretation for a given image pair. Psychophysical research has shown that binocular disparity stimuli displayed in 1 region of the visual field can be extrapolated into neighboring regions that contain ambiguous depth information. We tested whether neurons in macaque V1 interact in a similar manner and found that unambiguous binocular disparity stimuli displayed in the surrounding visual fields of disparity-selective V1 neurons indeed modified their responses when either bistable stereoscopic or uniform featureless stimuli were presented within their receptive field centers. The delayed timing of the response behavior compared with the timing of classical surround suppression and multiple control experiments suggests that these modulations are carried out by slower disparity-specific recurrent connections among V1 neurons. These results provide explicit evidence that the spatial interactions that are predicted by cooperative algorithms play an important role in solving the stereo correspondence problem.

Relating functional connectivity in V1 neural circuits and 3D natural scenes using Boltzmann machines

Bayesian theory has provided a compelling conceptualization for perceptual inference in the brain. Central to Bayesian inference is the notion of statistical priors. To understand the neural mechanisms of Bayesian inference, we need to understand the neural representation of statistical regularities in the natural environment. In this paper, we investigated empirically how statistical regularities in natural 3D scenes are represented in the functional connectivity of disparity-tuned neurons in the primary visual cortex of primates. We applied a Boltzmann machine model to learn from 3D natural scenes, and found that the units in the model exhibited cooperative and competitive interactions, forming a "disparity association field", analogous to the contour association field. The cooperative and competitive interactions in the disparity association field are consistent with constraints of computational models for stereo matching. In addition, we simulated neurophysiological experiments on the model, and found the results to be consistent with neurophysiological data in terms of the functional connectivity measurements between disparity-tuned neurons in the macaque primary visual cortex. These findings demonstrate that there is a relationship between the functional connectivity observed in the visual cortex and the statistics of natural scenes. They also suggest that the Boltzmann machine can be a viable model for conceptualizing computations in the visual cortex and, as such, can be used to predict neural circuits in the visual cortex from natural scene statistics.

The visual system's internal model of the world

The Bayesian paradigm has provided a useful conceptual theory for understanding perceptual computation in the brain. While the detailed neural mechanisms of Bayesian inference are not fully understood, recent computational and neurophysiological works have illuminated the underlying computational principles and representational architecture. The fundamental insights are that the visual system is organized as a modular hierarchy to encode an internal model of the world, and that perception is realized by statistical inference based on such internal model. In this paper, I will discuss and analyze the varieties of representational schemes of these internal models and how they might be used to perform learning and inference. I will argue for a unified theoretical framework for relating the internal models to the observed neural phenomena and mechanisms in the visual cortex.

Cross-matching: a modified cross-correlation underlying threshold energy model and match-based depth perception

Three-dimensional visual perception requires correct matching of images projected to the left and right eyes. The matching process is faced with an ambiguity: part of one eye's image can be matched to multiple parts of the other eye's image. This stereo correspondence problem is complicated for random-dot stereograms (RDSs), because dots with an identical appearance produce numerous potential matches. Despite such complexity, human subjects can perceive a coherent depth structure. A coherent solution to the correspondence problem does not exist for anticorrelated RDSs (aRDSs), in which luminance contrast is reversed in one eye. Neurons in the visual cortex reduce disparity selectivity for aRDSs progressively along the visual processing hierarchy. A disparity-energy model followed by threshold nonlinearity (threshold energy model) can account for this reduction, providing a possible mechanism for the neural matching process. However, the essential computation underlying the threshold energy model is not clear. Here, we propose that a nonlinear modification of cross-correlation, which we term “cross-matching,” represents the essence of the threshold energy model. We placed half-wave rectification within the cross-correlation of the left-eye and right-eye images. The disparity tuning derived from cross-matching was attenuated for aRDSs. We simulated a psychometric curve as a function of graded anticorrelation (graded mixture of aRDS and normal RDS); this simulated curve reproduced the match-based psychometric function observed in human near/far discrimination. The dot density was 25% for both simulation and observation. We predicted that as the dot density increased, the performance for aRDSs should decrease below chance (i.e., reversed depth), and the level of anticorrelation that nullifies depth perception should also decrease. We suggest that cross-matching serves as a simple computation underlying the match-based disparity signals in stereoscopic depth perception.

Sample skewness as a statistical measurement of neuronal tuning sharpness

We propose using the statistical measurement of the sample skewness of the distribution of mean firing rates of a tuning curve to quantify sharpness of tuning. For some features, like binocular disparity, tuning curves are best described by relatively complex and sometimes diverse functions, making it difficult to quantify sharpness with a single function and parameter. Skewness provides a robust nonparametric measure of tuning curve sharpness that is invariant with respect to the mean and variance of the tuning curve and is straightforward to apply to a wide range of tuning, including simple orientation tuning curves and complex object tuning curves that often cannot even be described parametrically. Because skewness does not depend on a specific model or function of tuning, it is especially appealing to cases of sharpening where recurrent interactions among neurons produce sharper tuning curves that deviate in a complex manner from the feedforward function of tuning. Since tuning curves for all neurons are not typically well described by a single parametric function, this model independence additionally allows skewness to be applied to all recorded neurons, maximizing the statistical power of a set of data. We also compare skewness with other nonparametric measures of tuning curve sharpness and selectivity. Compared to these other nonparametric measures tested, skewness is best used for capturing the sharpness of multimodal tuning curves defined by narrow peaks (maximum) and broad valleys (minima). Finally, we provide a more formal definition of sharpness using a shape-based information gain measure and derive and show that skewness is correlated with this definition.

Spatial and temporal scales of neuronal correlation in visual area V4

The spiking activity of nearby cortical neurons is correlated on both short and long time scales. Understanding this shared variability in firing patterns is critical for appreciating the representation of sensory stimuli in ensembles of neurons, the coincident influences of neurons on common targets, and the functional implications of microcircuitry. Our knowledge about neuronal correlations, however, derives largely from experiments that used different recording methods, analysis techniques, and cortical regions. Here we studied the structure of neuronal correlation in area V4 of alert macaques using recording and analysis procedures designed to match those used previously in primary visual cortex (V1), the major input to V4. We found that the spatial and temporal properties of correlations in V4 were remarkably similar to those of V1, with two notable differences: correlated variability in V4 was approximately one-third the magnitude of that in V1 and synchrony in V4 was less temporally precise than in V1. In both areas, spontaneous activity (measured during fixation while viewing a blank screen) was approximately twice as correlated as visual-evoked activity. The results provide a foundation for understanding how the structure of neuronal correlation differs among brain regions and stages in cortical processing and suggest that it is likely governed by features of neuronal circuits that are shared across the visual cortex.

Neural dynamics of image representation in the primary visual cortex

Horizontal connections in the primary visual cortex have been hypothesized to play a number of computational roles: association field for contour completion, surface interpolation, surround suppression, and saliency computation. Here, we argue that horizontal connections might also serve a critical role for computing the appropriate codes for image representation. That the early visual cortex or V1 explicitly represents the image we perceive has been a common assumption in computational theories of efficient coding (Olshausen and Field (1996)), yet such a framework for understanding the circuitry in V1 has not been seriously entertained in the neurophysiological community. In fact, a number of recent fMRI and neurophysiological studies cast doubt on the neural validity of such an isomorphic representation (Cornelissen et al., 2006; von der Heydt et al., 2003). In this study, we investigated, neurophysiologically, how V1 neurons respond to uniform color surfaces and show that spiking activities of neurons can be decomposed into three components: a bottom-up feedforward input, an articulation of color tuning and a contextual modulation signal that is inversely proportional to the distance away from the bounding contrast border. We demonstrate through computational simulations that the behaviors of a model for image representation are consistent with many aspects of our neural observations. We conclude that the hypothesis of isomorphic representation of images in V1 remains viable and this hypothesis suggests an additional new interpretation of the functional roles of horizontal connections in the primary visual cortex.

Correlated discharges in the primate prefrontal cortex before and after working memory training

The correlation of discharges between single neurons can provide information about the computations and network properties of neuronal populations during the performance of cognitive tasks. In recent years, dynamic modulation of neuronal correlations by attention has been revealed during the execution of behavioral tasks. Much less is known about the influence of learning and performing a task itself. We therefore sought to quantify the correlated firing of simultaneously recorded pairs of neurons in the prefrontal cortex of naïve monkeys that were only required to fixate, and to examine how this correlation was altered after they had learned to perform a working memory task. We found that the trial-to-trial correlation of discharge rates between pairs of neurons (noise correlation) differed across neurons depending on their responsiveness and selectivity for stimuli, even before training in a working memory task. After monkeys had learned to perform the task, correlated firing decreased overall, although the effects varied according to the functional properties of the neurons. The greatest decreases were observed on comparison of populations of neurons that exhibited elevated firing rates during the trial events and those that had more similar spatial and temporal tuning. Greater decreases in noise correlation were also observed for pairs comprising one fast spiking neuron (putative interneuron) and one regular spiking neuron (putative pyramidal neuron) than pairs comprising regular spiking neurons only. Our results demonstrate that learning and performance of a cognitive task alters the correlation structure of neuronal firing in the prefrontal cortex.

Decision-related activity in sensory neurons: correlations among neurons and with behavior

Neurons in early sensory cortex show weak but systematic correlations with perceptual decisions when trained animals perform at psychophysical threshold. These correlations are observed across repeated presentations of identical stimuli and cannot be explained by variation in external factors. The relationship between the activity of individual sensory neurons and the animal's behavioral choice means that even neurons in early sensory cortex carry information about an upcoming decision. This relationship, termed choice probability, may reflect the effect of fluctuations in neuronal firing rate on the animal's decision, but it can also reflect modulation of sensory responses by cognitive factors, or network properties such as variability that is shared among populations of neurons. Here, we review recent work clarifying the relationship among fluctuations in the responses of individual neurons, correlated variability, and behavior in a variety of tasks and cortical areas. We also discuss the possibility that choice probability may in part reflect the influence of cognitive factors on sensory neurons and explore the situations in which choice probability can be used to make inferences about the role of particular sensory neurons in the decision-making process.

Relative luminance and binocular disparity preferences are correlated in macaque primary visual cortex, matching natural scene statistics

Humans excel at inferring information about 3D scenes from their 2D images projected on the retinas, using a wide range of depth cues. One example of such inference is the tendency for observers to perceive lighter image regions as closer. This psychophysical behavior could have an ecological basis because nearer regions tend to be lighter in natural 3D scenes. Here, we show that an analogous association exists between the relative luminance and binocular disparity preferences of neurons in macaque primary visual cortex. The joint coding of relative luminance and binocular disparity at the neuronal population level may be an integral part of the neural mechanisms for perceptual inference of depth from images.

Measuring and interpreting neuronal correlations

Mounting evidence suggests that understanding how the brain encodes information and performs computations will require studying the correlations between neurons. The recent advent of recording techniques such as multielectrode arrays and two-photon imaging has made it easier to measure correlations, opening the door for detailed exploration of their properties and contributions to cortical processing. However, studies have reported discrepant findings, providing a confusing picture. Here we briefly review these studies and conduct simulations to explore the influence of several experimental and physiological factors on correlation measurements. Differences in response strength, the time window over which spikes are counted, spike sorting conventions and internal states can all markedly affect measured correlations and systematically bias estimates. Given these complicating factors, we offer guidelines for interpreting correlation data and a discussion of how best to evaluate the effect of correlations on cortical processing.

Triphasic dynamics of stimulus-dependent information flow between single neurons in macaque inferior temporal cortex

The functional connectivity between cortical neurons is not static and is known to exhibit contextual modulations in terms of the coupling strength. Here we hypothesized that the information flow in a cortical local circuit exhibits complex forward-and-back dynamics, and conducted Granger causality analysis between the neuronal spike trains that were simultaneously recorded from macaque inferior temporal (IT) cortex while the animals performed a visual object discrimination task. Spikes from neuron pairs with a displaced peak on the cross-correlogram (CCG) showed Granger causality in the gamma-frequency range (30-80 Hz) with the dominance in the direction consistent with the CCG peak (forward direction). Although, in a classical view, the displaced CCG peak has been interpreted as an indicative of a pauci-synaptic serial linkage, temporal dynamics of the gamma Granger causality after stimulus onset exhibited a more complex triphasic pattern, with a transient forward component followed by a slowly developing backward component and subsequent reappearance of the forward component. These triphasic dynamics of causality were not explained by the firing rate dynamics and were not observed for cell pairs that exhibited a center peak on the CCG. Furthermore, temporal dynamics of Granger causality depended on the feature configuration within the presented object. Together, these results demonstrate that the classical view of functional connectivity could be expanded to incorporate more complex forward-and-back dynamics and also imply that multistage processing in the recognition of visual objects might be implemented by multiphasic dynamics of directional information flow between single neurons in a local circuit in the IT cortex.