A network that uses few active neurones to code visual input predicts the diverse shapes of cortical receptive fields

Biologically Inspired Spatial-Temporal Perceiving Strategies for Spiking Neural Network

A future unmanned system needs the ability to perceive, decide and control in an open dynamic environment. In order to fulfill this requirement, it needs to construct a method with a universal environmental perception ability. Moreover, this perceptual process needs to be interpretable and understandable, so that future interactions between unmanned systems and humans can be unimpeded. However, current mainstream DNN (deep learning neural network)-based AI (artificial intelligence) is a 'black box'. We cannot interpret or understand how the decision is made by these AIs. An SNN (spiking neural network), which is more similar to a biological brain than a DNN, has the potential to implement interpretable or understandable AI. In this work, we propose a neuron group-based structural learning method for an SNN to better capture the spatial and temporal information from the external environment, and propose a time-slicing scheme to better interpret the spatial and temporal information of responses generated by an SNN. Results show that our method indeed helps to enhance the environment perception ability of the SNN, and possesses a certain degree of robustness, enhancing the potential to build an interpretable or understandable AI in the future.

Estimating receptive fields of simple and complex cells in early visual cortex: A convolutional neural network model with parameterized rectification

Neurons in the primary visual cortex respond selectively to simple features of visual stimuli, such as orientation and spatial frequency. Simple cells, which have phase-sensitive responses, can be modeled by a single receptive field filter in a linear-nonlinear model. However, it is challenging to analyze phase-invariant complex cells, which require more elaborate models having a combination of nonlinear subunits. Estimating parameters of these models is made additionally more difficult by cortical neurons' trial-to-trial response variability. We develop a simple convolutional neural network method to estimate receptive field models for both simple and complex visual cortex cells from their responses to natural images. The model consists of a spatiotemporal filter, a parameterized rectifier unit (PReLU), and a two-dimensional Gaussian "map" of the receptive field envelope. A single model parameter determines the simple vs. complex nature of the receptive field, capturing complex cell responses as a summation of homogeneous subunits, and collapsing to a linear-nonlinear model for simple type cells. The convolutional method predicts simple and complex cell responses to natural image stimuli as well as grating tuning curves. The fitted models yield a continuum of values for the PReLU parameter across the sampled neurons, showing that the simple/complex nature of cells can vary in a continuous manner. We demonstrate that complex-like cells respond less reliably than simple-like cells. However, compensation for this unreliability with noise ceiling analysis reveals predictive performance for complex cells proportionately closer to that for simple cells. Most spatial receptive field structures are well fit by Gabor functions, whose parameters confirm well-known properties of cat A17/18 receptive fields.

Brain-computer interface paradigms and neural coding

Brain signal patterns generated in the central nervous system of brain-computer interface (BCI) users are closely related to BCI paradigms and neural coding. In BCI systems, BCI paradigms and neural coding are critical elements for BCI research. However, so far there have been few references that clearly and systematically elaborated on the definition and design principles of the BCI paradigm as well as the definition and modeling principles of BCI neural coding. Therefore, these contents are expounded and the existing main BCI paradigms and neural coding are introduced in the review. Finally, the challenges and future research directions of BCI paradigm and neural coding were discussed, including user-centered design and evaluation for BCI paradigms and neural coding, revolutionizing the traditional BCI paradigms, breaking through the existing techniques for collecting brain signals and combining BCI technology with advanced AI technology to improve brain signal decoding performance. It is expected that the review will inspire innovative research and development of the BCI paradigm and neural coding.

Beyond ℓ1 sparse coding in V1

Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using the ℓ1 norm as a penalty due to its convexity, which makes it amenable to fast and simple algorithmic solvers. In this work, we use biological vision as a test-bed and show that the soft thresholding operation associated to the use of the ℓ1 norm is highly suboptimal compared to other functions suited to approximating ℓp with 0 ≤ p < 1 (including recently proposed continuous exact relaxations), in terms of performance. We show that ℓ1 sparsity employs a pool with more neurons, i.e. has a higher degree of overcompleteness, in order to maintain the same reconstruction error as the other methods considered. More specifically, at the same sparsity level, the thresholding algorithm using the ℓ1 norm as a penalty requires a dictionary of ten times more units compared to the proposed approach, where a non-convex continuous relaxation of the ℓ0 pseudo-norm is used, to reconstruct the external stimulus equally well. At a fixed sparsity level, both ℓ0- and ℓ1-based regularization develop units with receptive field (RF) shapes similar to biological neurons in V1 (and a subset of neurons in V2), but ℓ0-based regularization shows approximately five times better reconstruction of the stimulus. Our results in conjunction with recent metabolic findings indicate that for V1 to operate efficiently it should follow a coding regime which uses a regularization that is closer to the ℓ0 pseudo-norm rather than the ℓ1 one, and suggests a similar mode of operation for the sensory cortex in general.

Variable Binding for Sparse Distributed Representations: Theory and Applications

Variable binding is a cornerstone of symbolic reasoning and cognition. But how binding can be implemented in connectionist models has puzzled neuroscientists, cognitive psychologists, and neural network researchers for many decades. One type of connectionist model that naturally includes a binding operation is vector symbolic architectures (VSAs). In contrast to other proposals for variable binding, the binding operation in VSAs is dimensionality-preserving, which enables representing complex hierarchical data structures, such as trees, while avoiding a combinatoric expansion of dimensionality. Classical VSAs encode symbols by dense randomized vectors, in which information is distributed throughout the entire neuron population. By contrast, in the brain, features are encoded more locally, by the activity of single neurons or small groups of neurons, often forming sparse vectors of neural activation. Following Laiho et al. (2015), we explore symbolic reasoning with a special case of sparse distributed representations. Using techniques from compressed sensing, we first show that variable binding in classical VSAs is mathematically equivalent to tensor product binding between sparse feature vectors, another well-known binding operation which increases dimensionality. This theoretical result motivates us to study two dimensionality-preserving binding methods that include a reduction of the tensor matrix into a single sparse vector. One binding method for general sparse vectors uses random projections, the other, block-local circular convolution, is defined for sparse vectors with block structure, sparse block-codes. Our experiments reveal that block-local circular convolution binding has ideal properties, whereas random projection based binding also works, but is lossy. We demonstrate in example applications that a VSA with block-local circular convolution and sparse block-codes reaches similar performance as classical VSAs. Finally, we discuss our results in the context of neuroscience and neural networks.

Diversity of spatiotemporal coding reveals specialized visual processing streams in the mouse cortex

The cerebral cortex contains diverse neural representations of the visual scene, each enabling distinct visual and spatial abilities. However, the extent to which representations are distributed or segregated across cortical areas remains poorly understood. By determining the spatial and temporal responses of >30,000 layer 2/3 pyramidal neurons, we characterize the functional organization of parallel visual streams across eight areas of the mouse cortex. While dorsal and ventral areas form complementary representations of spatiotemporal frequency, motion speed, and spatial patterns, the anterior and posterior dorsal areas show distinct specializations for fast and slow oriented contrasts. At the cellular level, while diverse spatiotemporal tuning lies along a continuum, oriented and non-oriented spatial patterns are encoded by distinct tuning types. The identified tuning types are present across dorsal and ventral streams. The data underscore the highly specific and highly distributed nature of visual cortical representations, which drives specialization of cortical areas and streams.

The cerebral cortex contains different neural representations of the visual scene. Here, the authors show diverse and stereotyped tuning composing specialized representations in the dorsal and ventral areas of the mouse visual cortex, suggesting parallel processing channels and streams.

Constrained brain volume in an efficient coding model explains the fraction of excitatory and inhibitory neurons in sensory cortices

The number of neurons in mammalian cortex varies by multiple orders of magnitude across different species. In contrast, the ratio of excitatory to inhibitory neurons (E:I ratio) varies in a much smaller range, from 3:1 to 9:1 and remains roughly constant for different sensory areas within a species. Despite this structure being important for understanding the function of neural circuits, the reason for this consistency is not yet understood. While recent models of vision based on the efficient coding hypothesis show that increasing the number of both excitatory and inhibitory cells improves stimulus representation, the two cannot increase simultaneously due to constraints on brain volume. In this work, we implement an efficient coding model of vision under a constraint on the volume (using number of neurons as a surrogate) while varying the E:I ratio. We show that the performance of the model is optimal at biologically observed E:I ratios under several metrics. We argue that this happens due to trade-offs between the computational accuracy and the representation capacity for natural stimuli. Further, we make experimentally testable predictions that 1) the optimal E:I ratio should be higher for species with a higher sparsity in the neural activity and 2) the character of inhibitory synaptic distributions and firing rates should change depending on E:I ratio. Our findings, which are supported by our new preliminary analyses of publicly available data, provide the first quantitative and testable hypothesis based on optimal coding models for the distribution of excitatory and inhibitory neural types in the mammalian sensory cortices.

Neurons in the brain come in two main types: excitatory and inhibitory. The interplay between them shapes neural computation. Despite brain sizes varying by several orders of magnitude across species, the ratio of excitatory and inhibitory sub-populations (E:I ratio) remains relatively constant, and we don’t know why. Simulations of theoretical models of the brain can help answer such questions, especially when experiments are prohibitive or impossible. Here we placed one such theoretical model of sensory coding (’sparse coding’ that minimizes the simultaneously active neurons) under a biophysical ‘volume’ constraint that fixes the total number of neurons available. We vary the E:I ratio in the model (which cannot be done in experiments), and reveal an optimal E:I ratio where the representation of sensory stimulus and energy consumption within the circuit are concurrently optimal. We also show that varying the population sparsity changes the optimal E:I ratio, spanning the relatively narrow ranges observed in biology. Crucially, this minimally parameterized theoretical model makes predictions about structure (recurrent connectivity) and activity (population sparsity) in neural circuits with different E:I ratios (i.e., different species), of which we verify the latter in a first-of-its-kind inter-species comparison using newly publicly available data.

Sub-Optimality of the Early Visual System Explained Through Biologically Plausible Plasticity

The early visual cortex is the site of crucial pre-processing for more complex, biologically relevant computations that drive perception and, ultimately, behaviour. This pre-processing is often studied under the assumption that neural populations are optimised for the most efficient (in terms of energy, information, spikes, etc.) representation of natural statistics. Normative models such as Independent Component Analysis (ICA) and Sparse Coding (SC) consider the phenomenon as a generative, minimisation problem which they assume the early cortical populations have evolved to solve. However, measurements in monkey and cat suggest that receptive fields (RFs) in the primary visual cortex are often noisy, blobby, and symmetrical, making them sub-optimal for operations such as edge-detection. We propose that this suboptimality occurs because the RFs do not emerge through a global minimisation of generative error, but through locally operating biological mechanisms such as spike-timing dependent plasticity (STDP). Using a network endowed with an abstract, rank-based STDP rule, we show that the shape and orientation tuning of the converged units are remarkably close to single-cell measurements in the macaque primary visual cortex. We quantify this similarity using physiological parameters (frequency-normalised spread vectors), information theoretic measures [Kullback–Leibler (KL) divergence and Gini index], as well as simulations of a typical electrophysiology experiment designed to estimate orientation tuning curves. Taken together, our results suggest that compared to purely generative schemes, process-based biophysical models may offer a better description of the suboptimality observed in the early visual cortex.

Complexity and diversity in sparse code priors improve receptive field characterization of Macaque V1 neurons

System identification techniques-projection pursuit regression models (PPRs) and convolutional neural networks (CNNs)-provide state-of-the-art performance in predicting visual cortical neurons' responses to arbitrary input stimuli. However, the constituent kernels recovered by these methods are often noisy and lack coherent structure, making it difficult to understand the underlying component features of a neuron's receptive field. In this paper, we show that using a dictionary of diverse kernels with complex shapes learned from natural scenes based on efficient coding theory, as the front-end for PPRs and CNNs can improve their performance in neuronal response prediction as well as algorithmic data efficiency and convergence speed. Extensive experimental results also indicate that these sparse-code kernels provide important information on the component features of a neuron's receptive field. In addition, we find that models with the complex-shaped sparse code front-end are significantly better than models with a standard orientation-selective Gabor filter front-end for modeling V1 neurons that have been found to exhibit complex pattern selectivity. We show that the relative performance difference due to these two front-ends can be used to produce a sensitive metric for detecting complex selectivity in V1 neurons.

Sparsely Activated Networks

Previous literature on unsupervised learning focused on designing structural priors with the aim of learning meaningful features. However, this was done without considering the description length of the learned representations, which is a direct and unbiased measure of the model complexity. In this article, first, we introduce the φ metric that evaluates unsupervised models based on their reconstruction accuracy and the degree of compression of their internal representations. We then present and define two activation functions [Identity and rectified linear unit (ReLU)] as a base of reference and three sparse activation functions (top-k absolutes, Extrema-Pool indices, and Extrema) as candidate structures that minimize the previously defined φ . We last present sparsely activated networks (SANs) that consist of kernels with shared weights that, during encoding, are convolved with the input and then passed through a sparse activation function. During decoding, the same weights are convolved with the sparse activation map, and subsequently, the partial reconstructions from each weight are summed to reconstruct the input. We compare SANs using the five previously defined activation functions on a variety of data sets (Physionet, UCI-epilepsy, MNIST, and FMNIST) and show that models that are selected using φ have small description representation length and consist of interpretable kernels.

Exploitation of image statistics with sparse coding in the case of stereo vision

The sparse coding algorithm has served as a model for early processing in mammalian vision. It has been assumed that the brain uses sparse coding to exploit statistical properties of the sensory stream. We hypothesize that sparse coding discovers patterns from the data set, which can be used to estimate a set of stimulus parameters by simple readout. In this study, we chose a model of stereo vision to test our hypothesis. We used the Locally Competitive Algorithm (LCA), followed by a naïve Bayes classifier, to infer stereo disparity. From the results we report three observations. First, disparity inference was successful with this naturalistic processing pipeline. Second, an expanded, highly redundant representation is required to robustly identify the input patterns. Third, the inference error can be predicted from the number of active coefficients in the LCA representation. We conclude that sparse coding can generate a suitable general representation for subsequent inference tasks.

Spatio-chromatic information available from different neural layers via Gaussianization

How much visual information about the retinal images can be extracted from the different layers of the visual pathway? This question depends on the complexity of the visual input, the set of transforms applied to this multivariate input, and the noise of the sensors in the considered layer. Separate subsystems (e.g. opponent channels, spatial filters, nonlinearities of the texture sensors) have been suggested to be organized for optimal information transmission. However, the efficiency of these different layers has not been measured when they operate together on colorimetrically calibrated natural images and using multivariate information-theoretic units over the joint spatio-chromatic array of responses.In this work, we present a statistical tool to address this question in an appropriate (multivariate) way. Specifically, we propose an empirical estimate of the information transmitted by the system based on a recent Gaussianization technique. The total correlation measured using the proposed estimator is consistent with predictions based on the analytical Jacobian of a standard spatio-chromatic model of the retina-cortex pathway. If the noise at certain representation is proportional to the dynamic range of the response, and one assumes sensors of equivalent noise level, then transmitted information shows the following trends: (1) progressively deeper representations are better in terms of the amount of captured information, (2) the transmitted information up to the cortical representation follows the probability of natural scenes over the chromatic and achromatic dimensions of the stimulus space, (3) the contribution of spatial transforms to capture visual information is substantially greater than the contribution of chromatic transforms, and (4) nonlinearities of the responses contribute substantially to the transmitted information but less than the linear transforms.

The statistics of how natural images drive the responses of neurons

To model the responses of neurons in the early visual system, at least three basic components are required: a receptive field, a normalization term, and a specification of encoding noise. Here, we examine how the receptive field, the normalization factor, and the encoding noise affect the drive to model-neuron responses when stimulated with natural images. We show that when these components are modeled appropriately, the response drives elicited by natural stimuli are Gaussian-distributed and scale invariant, and very nearly maximize the sensitivity (d') for natural-image discrimination. We discuss the statistical models of natural stimuli that can account for these response statistics, and we show how some commonly used modeling practices may distort these results. Finally, we show that normalization can equalize important properties of neural response across different stimulus types. Specifically, narrowband (stimulus- and feature-specific) normalization causes model neurons to yield Gaussian response-drive statistics when stimulated with natural stimuli, 1/f noise stimuli, and white-noise stimuli. The current work makes recommendations for best practices and lays a foundation, grounded in the response statistics to natural stimuli, upon which to build principled models of more complex visual tasks.

Natural images are reliably represented by sparse and variable populations of neurons in visual cortex

Natural scenes sparsely activate neurons in the primary visual cortex (V1). However, how sparsely active neurons reliably represent complex natural images and how the information is optimally decoded from these representations have not been revealed. Using two-photon calcium imaging, we recorded visual responses to natural images from several hundred V1 neurons and reconstructed the images from neural activity in anesthetized and awake mice. A single natural image is linearly decodable from a surprisingly small number of highly responsive neurons, and the remaining neurons even degrade the decoding. Furthermore, these neurons reliably represent the image across trials, regardless of trial-to-trial response variability. Based on our results, diverse, partially overlapping receptive fields ensure sparse and reliable representation. We suggest that information is reliably represented while the corresponding neuronal patterns change across trials and collecting only the activity of highly responsive neurons is an optimal decoding strategy for the downstream neurons.

Constrained inference in sparse coding reproduces contextual effects and predicts laminar neural dynamics

When probed with complex stimuli that extend beyond their classical receptive field, neurons in primary visual cortex display complex and non-linear response characteristics. Sparse coding models reproduce some of the observed contextual effects, but still fail to provide a satisfactory explanation in terms of realistic neural structures and cortical mechanisms, since the connection scheme they propose consists only of interactions among neurons with overlapping input fields. Here we propose an extended generative model for visual scenes that includes spatial dependencies among different features. We derive a neurophysiologically realistic inference scheme under the constraint that neurons have direct access only to local image information. The scheme can be interpreted as a network in primary visual cortex where two neural populations are organized in different layers within orientation hypercolumns that are connected by local, short-range and long-range recurrent interactions. When trained with natural images, the model predicts a connectivity structure linking neurons with similar orientation preferences matching the typical patterns found for long-ranging horizontal axons and feedback projections in visual cortex. Subjected to contextual stimuli typically used in empirical studies, our model replicates several hallmark effects of contextual processing and predicts characteristic differences for surround modulation between the two model populations. In summary, our model provides a novel framework for contextual processing in the visual system proposing a well-defined functional role for horizontal axons and feedback projections.

An Adaptive Homeostatic Algorithm for the Unsupervised Learning of Visual Features

The formation of structure in the visual system, that is, of the connections between cells within neural populations, is by and large an unsupervised learning process. In the primary visual cortex of mammals, for example, one can observe during development the formation of cells selective to localized, oriented features, which results in the development of a representation in area V1 of images’ edges. This can be modeled using a sparse Hebbian learning algorithms which alternate a coding step to encode the information with a learning step to find the proper encoder. A major difficulty of such algorithms is the joint problem of finding a good representation while knowing immature encoders, and to learn good encoders with a nonoptimal representation. To solve this problem, this work introduces a new regulation process between learning and coding which is motivated by the homeostasis processes observed in biology. Such an optimal homeostasis rule is implemented by including an adaptation mechanism based on nonlinear functions that balance the antagonistic processes that occur at the coding and learning time scales. It is compatible with a neuromimetic architecture and allows for a more efficient emergence of localized filters sensitive to orientation. In addition, this homeostasis rule is simplified by implementing a simple heuristic on the probability of activation of neurons. Compared to the optimal homeostasis rule, numerical simulations show that this heuristic allows to implement a faster unsupervised learning algorithm while retaining much of its effectiveness. These results demonstrate the potential application of such a strategy in machine learning and this is illustrated by showing the effect of homeostasis in the emergence of edge-like filters for a convolutional neural network.

On the Sparse Structure of Natural Sounds and Natural Images: Similarities, Differences, and Implications for Neural Coding

Sparse coding models of natural images and sounds have been able to predict several response properties of neurons in the visual and auditory systems. While the success of these models suggests that the structure they capture is universal across domains to some degree, it is not yet clear which aspects of this structure are universal and which vary across sensory modalities. To address this, we fit complete and highly overcomplete sparse coding models to natural images and spectrograms of speech and report on differences in the statistics learned by these models. We find several types of sparse features in natural images, which all appear in similar, approximately Laplace distributions, whereas the many types of sparse features in speech exhibit a broad range of sparse distributions, many of which are highly asymmetric. Moreover, individual sparse coding units tend to exhibit higher lifetime sparseness for overcomplete models trained on images compared to those trained on speech. Conversely, population sparseness tends to be greater for these networks trained on speech compared with sparse coding models of natural images. To illustrate the relevance of these findings to neural coding, we studied how they impact a biologically plausible sparse coding network's representations in each sensory modality. In particular, a sparse coding network with synaptically local plasticity rules learns different sparse features from speech data than are found by more conventional sparse coding algorithms, but the learned features are qualitatively the same for these models when trained on natural images.

Neural correlates of sparse coding and dimensionality reduction

Supported by recent computational studies, there is increasing evidence that a wide range of neuronal responses can be understood as an emergent property of nonnegative sparse coding (NSC), an efficient population coding scheme based on dimensionality reduction and sparsity constraints. We review evidence that NSC might be employed by sensory areas to efficiently encode external stimulus spaces, by some associative areas to conjunctively represent multiple behaviorally relevant variables, and possibly by the basal ganglia to coordinate movement. In addition, NSC might provide a useful theoretical framework under which to understand the often complex and nonintuitive response properties of neurons in other brain areas. Although NSC might not apply to all brain areas (for example, motor or executive function areas) the success of NSC-based models, especially in sensory areas, warrants further investigation for neural correlates in other regions.

Toward a Biologically Plausible Model of LGN-V1 Pathways Based on Efficient Coding

Increasing evidence supports the hypothesis that the visual system employs a sparse code to represent visual stimuli, where information is encoded in an efficient way by a small population of cells that respond to sensory input at a given time. This includes simple cells in primary visual cortex (V1), which are defined by their linear spatial integration of visual stimuli. Various models of sparse coding have been proposed to explain physiological phenomena observed in simple cells. However, these models have usually made the simplifying assumption that inputs to simple cells already incorporate linear spatial summation. This overlooks the fact that these inputs are known to have strong non-linearities such the separation of ON and OFF pathways, or separation of excitatory and inhibitory neurons. Consequently these models ignore a range of important experimental phenomena that are related to the emergence of linear spatial summation from non-linear inputs, such as segregation of ON and OFF sub-regions of simple cell receptive fields, the push-pull effect of excitation and inhibition, and phase-reversed cortico-thalamic feedback. Here, we demonstrate that a two-layer model of the visual pathway from the lateral geniculate nucleus to V1 that incorporates these biological constraints on the neural circuits and is based on sparse coding can account for the emergence of these experimental phenomena, diverse shapes of receptive fields and contrast invariance of orientation tuning of simple cells when the model is trained on natural images. The model suggests that sparse coding can be implemented by the V1 simple cells using neural circuits with a simple biologically plausible architecture.

Normalization and pooling in hierarchical models of natural images

Divisive normalization and subunit pooling are two canonical classes of computation that have become widely used in descriptive (what) models of visual cortical processing. Normative (why) models from natural image statistics can help constrain the form and parameters of such classes of models. We focus on recent advances in two particular directions, namely deriving richer forms of divisive normalization, and advances in learning pooling from image statistics. We discuss the incorporation of such components into hierarchical models. We consider both hierarchical unsupervised learning from image statistics, and discriminative supervised learning in deep convolutional neural networks (CNNs). We further discuss studies on the utility and extensions of the convolutional architecture, which has also been adopted by recent descriptive models. We review the recent literature and discuss the current promises and gaps of using such approaches to gain a better understanding of how cortical neurons represent and process complex visual stimuli.

Cortical Visual Performance Test Setup for Parkinson's Disease Based on Motion Blur Orientation

Studies on Parkinson's disease (PD) are becoming very popular on multidisciplinary platforms. The development of predictable telemonitored early detection models has become closely related to many different research areas. The aim of this article is to develop a visual performance test that can examine the effects of Parkinson's disease on the visual cortex, which can be a subtitle scoring test in UPDRS. However, instead of showing random images and asking for discrepancies between them, it is expected that the questions to be asked to patients should be provable in the existing cortex models, should be deduced between the images, and produce a reference threshold value to compare with the practical results. In a developed test, horizontal and vertical motion blur orientation was applied to natural image samples, and then neural outputs were produced by representing three (original-horizontal-vertical) image groups with the Layer 4 (L4) cortex model. This image representation is then compared with a filtering model which is very similar to thalamus' functionality. Thus, the linear problem-solving performance of the L4 cortex model is also addressed in the study. According to the obtained classification results, the L4 model produces high-performance success rates compared to the thalamic model, which shows the adaptation power of the visual cortex on the image pattern differences. In future studies, developed motion-based visual tests are planned to be applied to PD patient groups/controls, and their performances with mathematical threshold values will be examined.

Stimulus- and goal-oriented frameworks for understanding natural vision

Our knowledge of sensory processing has advanced dramatically in the last few decades, but this understanding remains far from complete, especially for stimuli with the large dynamic range and strong temporal and spatial correlations characteristic of natural visual inputs. Here we describe some of the issues that make understanding the encoding of natural images a challenge. We highlight two broad strategies for approaching this problem: a stimulus-oriented framework and a goal-oriented one. Different contexts can call for one framework or the other. Looking forward, recent advances, particularly those based in machine learning, show promise in borrowing key strengths of both frameworks and by doing so illuminating a path to a more comprehensive understanding of the encoding of natural stimuli.

Deep learning in spiking neural networks

In recent years, deep learning has revolutionized the field of machine learning, for computer vision in particular. In this approach, a deep (multilayer) artificial neural network (ANN) is trained, most often in a supervised manner using backpropagation. Vast amounts of labeled training examples are required, but the resulting classification accuracy is truly impressive, sometimes outperforming humans. Neurons in an ANN are characterized by a single, static, continuous-valued activation. Yet biological neurons use discrete spikes to compute and transmit information, and the spike times, in addition to the spike rates, matter. Spiking neural networks (SNNs) are thus more biologically realistic than ANNs, and are arguably the only viable option if one wants to understand how the brain computes at the neuronal description level. The spikes of biological neurons are sparse in time and space, and event-driven. Combined with bio-plausible local learning rules, this makes it easier to build low-power, neuromorphic hardware for SNNs. However, training deep SNNs remains a challenge. Spiking neurons' transfer function is usually non-differentiable, which prevents using backpropagation. Here we review recent supervised and unsupervised methods to train deep SNNs, and compare them in terms of accuracy and computational cost. The emerging picture is that SNNs still lag behind ANNs in terms of accuracy, but the gap is decreasing, and can even vanish on some tasks, while SNNs typically require many fewer operations and are the better candidates to process spatio-temporal data.

Large-scale two-photon imaging revealed super-sparse population codes in the V1 superficial layer of awake monkeys

One general principle of sensory information processing is that the brain must optimize efficiency by reducing the number of neurons that process the same information. The sparseness of the sensory representations in a population of neurons reflects the efficiency of the neural code. Here, we employ large-scale two-photon calcium imaging to examine the responses of a large population of neurons within the superficial layers of area V1 with single-cell resolution, while simultaneously presenting a large set of natural visual stimuli, to provide the first direct measure of the population sparseness in awake primates. The results show that only 0.5% of neurons respond strongly to any given natural image - indicating a ten-fold increase in the inferred sparseness over previous measurements. These population activities are nevertheless necessary and sufficient to discriminate visual stimuli with high accuracy, suggesting that the neural code in the primary visual cortex is both super-sparse and highly efficient.

Extracting neuronal functional network dynamics via adaptive Granger causality analysis

Quantifying the functional relations between the nodes in a network based on local observations is a key challenge in studying complex systems. Most existing time series analysis techniques for this purpose provide static estimates of the network properties, pertain to stationary Gaussian data, or do not take into account the ubiquitous sparsity in the underlying functional networks. When applied to spike recordings from neuronal ensembles undergoing rapid task-dependent dynamics, they thus hinder a precise statistical characterization of the dynamic neuronal functional networks underlying adaptive behavior. We develop a dynamic estimation and inference paradigm for extracting functional neuronal network dynamics in the sense of Granger, by integrating techniques from adaptive filtering, compressed sensing, point process theory, and high-dimensional statistics. We demonstrate the utility of our proposed paradigm through theoretical analysis, algorithm development, and application to synthetic and real data. Application of our techniques to two-photon Ca²⁺ imaging experiments from the mouse auditory cortex reveals unique features of the functional neuronal network structures underlying spontaneous activity at unprecedented spatiotemporal resolution. Our analysis of simultaneous recordings from the ferret auditory and prefrontal cortical areas suggests evidence for the role of rapid top-down and bottom-up functional dynamics across these areas involved in robust attentive behavior.

Small Networks Encode Decision-Making in Primary Auditory Cortex

Sensory detection tasks enhance representations of behaviorally meaningful stimuli in primary auditory cortex (A1). However, it remains unclear how A1 encodes decision-making. Neurons in A1 layer 2/3 (L2/3) show heterogeneous stimulus selectivity and complex anatomical connectivity, and receive input from prefrontal cortex. Thus, task-related modulation of activity in A1 L2/3 might differ across subpopulations. To study the neural coding of decision-making, we used two-photon imaging in A1 L2/3 of mice performing a tone-detection task. Neural responses to targets showed attentional gain and encoded behavioral choice. To characterize network representation of behavioral choice, we analyzed functional connectivity using Granger causality, pairwise noise correlations, and neural decoding. During task performance, small groups of four to five neurons became sparsely linked, locally clustered, and rostro-caudally oriented, while noise correlations both increased and decreased. Our results suggest that sensory-based decision-making involves small neural networks driven by the sum of sensory input, attentional gain, and behavioral choice.

Discrete Sparse Coding

Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.

The Two-Dimensional Gabor Function Adapted to Natural Image Statistics: A Model of Simple-Cell Receptive Fields and Sparse Structure in Images

The two-dimensional Gabor function is adapted to natural image statistics, leading to a tractable probabilistic generative model that can be used to model simple cell receptive field profiles, or generate basis functions for sparse coding applications. Learning is found to be most pronounced in three Gabor function parameters representing the size and spatial frequency of the two-dimensional Gabor function and characterized by a nonuniform probability distribution with heavy tails. All three parameters are found to be strongly correlated, resulting in a basis of multiscale Gabor functions with similar aspect ratios and size-dependent spatial frequencies. A key finding is that the distribution of receptive-field sizes is scale invariant over a wide range of values, so there is no characteristic receptive field size selected by natural image statistics. The Gabor function aspect ratio is found to be approximately conserved by the learning rules and is therefore not well determined by natural image statistics. This allows for three distinct solutions: a basis of Gabor functions with sharp orientation resolution at the expense of spatial-frequency resolution, a basis of Gabor functions with sharp spatial-frequency resolution at the expense of orientation resolution, or a basis with unit aspect ratio. Arbitrary mixtures of all three cases are also possible. Two parameters controlling the shape of the marginal distributions in a probabilistic generative model fully account for all three solutions. The best-performing probabilistic generative model for sparse coding applications is found to be a gaussian copula with Pareto marginal probability density functions.

Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities.

The question of how the brain self-organizes to develop precisely tuned neurons has puzzled neuroscientists at least since the discoveries of Hubel and Wiesel. In the past decades, a variety of theories and models have been proposed to describe receptive field formation, notably V1 simple cells, from natural inputs. We cut through the jungle of candidate explanations by demonstrating that in fact a single principle is sufficient to explain receptive field development. Our results follow from two major insights. First, we show that many representative models of sensory development are in fact implementing variations of a common principle: nonlinear Hebbian learning. Second, we reveal that nonlinear Hebbian learning is sufficient for receptive field formation through sensory inputs. The surprising result is that our findings are robust of specific details of a model, and allows for robust predictions on the learned receptive fields. Nonlinear Hebbian learning is therefore general in two senses: it applies to many models developed by theoreticians, and to many sensory modalities studied by experimental neuroscientists.

Categorically distinct types of receptive fields in early visual cortex

In the visual cortex, distinct types of neurons have been identified based on cellular morphology, response to injected current, or expression of specific markers, but neurophysiological studies have revealed visual receptive field (RF) properties that appear to be on a continuum, with only two generally recognized classes: simple and complex. Most previous studies have characterized visual responses of neurons using stereotyped stimuli such as bars, gratings, or white noise and simple system identification approaches (e.g., reverse correlation). Here we estimate visual RF models of cortical neurons using visually rich natural image stimuli and regularized regression system identification methods and characterize their spatial tuning, temporal dynamics, spatiotemporal behavior, and spiking properties. We quantitatively demonstrate the existence of three functionally distinct categories of simple cells, distinguished by their degree of orientation selectivity (isotropic or oriented) and the nature of their output nonlinearity (expansive or compressive). In addition, these three types have differing average values of several other properties. Cells with nonoriented RFs tend to have smaller RFs, shorter response durations, no direction selectivity, and high reliability. Orientation-selective neurons with an expansive output nonlinearity have Gabor-like RFs, lower spontaneous activity and responsivity, and spiking responses with higher sparseness. Oriented RFs with a compressive nonlinearity are spatially nondescript and tend to show longer response latency. Our findings indicate multiple physiologically defined types of RFs beyond the simple/complex dichotomy, suggesting that cortical neurons may have more specialized functional roles rather than lying on a multidimensional continuum.

Modeling Inhibitory Interneurons in Efficient Sensory Coding Models

There is still much unknown regarding the computational role of inhibitory cells in the sensory cortex. While modeling studies could potentially shed light on the critical role played by inhibition in cortical computation, there is a gap between the simplicity of many models of sensory coding and the biological complexity of the inhibitory subpopulation. In particular, many models do not respect that inhibition must be implemented in a separate subpopulation, with those inhibitory interneurons having a diversity of tuning properties and characteristic E/I cell ratios. In this study we demonstrate a computational framework for implementing inhibition in dynamical systems models that better respects these biophysical observations about inhibitory interneurons. The main approach leverages recent work related to decomposing matrices into low-rank and sparse components via convex optimization, and explicitly exploits the fact that models and input statistics often have low-dimensional structure that can be exploited for efficient implementations. While this approach is applicable to a wide range of sensory coding models (including a family of models based on Bayesian inference in a linear generative model), for concreteness we demonstrate the approach on a network implementing sparse coding. We show that the resulting implementation stays faithful to the original coding goals while using inhibitory interneurons that are much more biophysically plausible.

Cortical function is a result of coordinated interactions between excitatory and inhibitory neural populations. In previous theoretical models of sensory systems, inhibitory neurons are often ignored or modeled too simplistically to contribute to understanding their role in cortical computation. In biophysical reality, inhibition is implemented with interneurons that have different characteristics from the population of excitatory cells. In this study, we propose a computational approach for including inhibition in theoretical models of neural coding in a way that respects several of these important characteristics, such as the relative number of inhibitory cells and the diversity of their response properties. The main idea is that the significant structure of the sensory world is reflected in very structured models of sensory coding, which can then be exploited in the implementation of the model using modern computational techniques. We demonstrate this approach on one specific model of sensory coding (called “sparse coding”) that has been successful at modeling other aspects of sensory cortex.

Competition improves robustness against loss of information

A substantial number of works have aimed at modeling the receptive field properties of the primary visual cortex (V1). Their evaluation criterion is usually the similarity of the model response properties to the recorded responses from biological organisms. However, as several algorithms were able to demonstrate some degree of similarity to biological data based on the existing criteria, we focus on the robustness against loss of information in the form of occlusions as an additional constraint for better understanding the algorithmic level of early vision in the brain. We try to investigate the influence of competition mechanisms on the robustness. Therefore, we compared four methods employing different competition mechanisms, namely, independent component analysis, non-negative matrix factorization with sparseness constraint, predictive coding/biased competition, and a Hebbian neural network with lateral inhibitory connections. Each of those methods is known to be capable of developing receptive fields comparable to those of V1 simple-cells. Since measuring the robustness of methods having simple-cell like receptive fields against occlusion is difficult, we measure the robustness using the classification accuracy on the MNIST hand written digit dataset. For this we trained all methods on the training set of the MNIST hand written digits dataset and tested them on a MNIST test set with different levels of occlusions. We observe that methods which employ competitive mechanisms have higher robustness against loss of information. Also the kind of the competition mechanisms plays an important role in robustness. Global feedback inhibition as employed in predictive coding/biased competition has an advantage compared to local lateral inhibition learned by an anti-Hebb rule.

Anatomical constraints on lateral competition in columnar cortical architectures

Competition is a well-studied and powerful mechanism for information processing in neuronal networks, providing noise rejection, signal restoration, decision making and associative memory properties, with relatively simple requirements for network architecture. Models based on competitive interactions have been used to describe the shaping of functional properties in visual cortex, as well as the development of functional maps in columnar cortex. These models require competition within a cortical area to occur on a wider spatial scale than cooperation, usually implemented by lateral inhibitory connections having a longer range than local excitatory connections. However, measurements of cortical anatomy reveal that the spatial extent of inhibition is in fact more restricted than that of excitation. Relatively few models reflect this, and it is unknown whether lateral competition can occur in cortical-like networks that have a realistic spatial relationship between excitation and inhibition. Here we analyze simple models for cortical columns and perform simulations of larger models to show how the spatial scales of excitation and inhibition can interact to produce competition through disynaptic inhibition. Our findings give strong support to the direct coupling effect-that the presence of competition across the cortical surface is predicted well by the anatomy of direct excitatory and inhibitory coupling and that multisynaptic network effects are negligible. This implies that for networks with short-range inhibition and longer-range excitation, the spatial extent of competition is even narrower than the range of inhibitory connections. Our results suggest the presence of network mechanisms that focus on intra-rather than intercolumn competition in neocortex, highlighting the need for both new models and direct experimental characterizations of lateral inhibition and competition in columnar cortex.

OPTIMAL SPARSE APPROXIMATION WITH INTEGRATE AND FIRE NEURONS

Sparse approximation is a hypothesized coding strategy where a population of sensory neurons (e.g. V1) encodes a stimulus using as few active neurons as possible. We present the Spiking LCA (locally competitive algorithm), a rate encoded Spiking Neural Network (SNN) of integrate and fire neurons that calculate sparse approximations. The Spiking LCA is designed to be equivalent to the nonspiking LCA, an analog dynamical system that converges on a ℓ1-norm sparse approximations exponentially. We show that the firing rate of the Spiking LCA converges on the same solution as the analog LCA, with an error inversely proportional to the sampling time. We simulate in NEURON a network of 128 neuron pairs that encode 8 × 8 pixel image patches, demonstrating that the network converges to nearly optimal encodings within 20 ms of biological time. We also show that when using more biophysically realistic parameters in the neurons, the gain function encourages additional ℓ0-norm sparsity in the encoding, relative both to ideal neurons and digital solvers.

Short-term memory capacity in networks via the restricted isometry property

Cortical networks are hypothesized to rely on transient network activity to support short-term memory (STM). In this letter, we study the capacity of randomly connected recurrent linear networks for performing STM when the input signals are approximately sparse in some basis. We leverage results from compressed sensing to provide rigorous nonasymptotic recovery guarantees, quantifying the impact of the input sparsity level, the input sparsity basis, and the network characteristics on the system capacity. Our analysis demonstrates that network memory capacities can scale superlinearly with the number of nodes and in some situations can achieve STM capacities that are much larger than the network size. We provide perfect recovery guarantees for finite sequences and recovery bounds for infinite sequences. The latter analysis predicts that network STM systems may have an optimal recovery length that balances errors due to omission and recall mistakes. Furthermore, we show that the conditions yielding optimal STM capacity can be embodied in several network topologies, including networks with sparse or dense connectivities.

Efficient coding of spectrotemporal binaural sounds leads to emergence of the auditory space representation

To date a number of studies have shown that receptive field shapes of early sensory neurons can be reproduced by optimizing coding efficiency of natural stimulus ensembles. A still unresolved question is whether the efficient coding hypothesis explains formation of neurons which explicitly represent environmental features of different functional importance. This paper proposes that the spatial selectivity of higher auditory neurons emerges as a direct consequence of learning efficient codes for natural binaural sounds. Firstly, it is demonstrated that a linear efficient coding transform—Independent Component Analysis (ICA) trained on spectrograms of naturalistic simulated binaural sounds extracts spatial information present in the signal. A simple hierarchical ICA extension allowing for decoding of sound position is proposed. Furthermore, it is shown that units revealing spatial selectivity can be learned from a binaural recording of a natural auditory scene. In both cases a relatively small subpopulation of learned spectrogram features suffices to perform accurate sound localization. Representation of the auditory space is therefore learned in a purely unsupervised way by maximizing the coding efficiency and without any task-specific constraints. This results imply that efficient coding is a useful strategy for learning structures which allow for making behaviorally vital inferences about the environment.

Spatio-chromatic adaptation via higher-order canonical correlation analysis of natural images

Independent component and canonical correlation analysis are two general-purpose statistical methods with wide applicability. In neuroscience, independent component analysis of chromatic natural images explains the spatio-chromatic structure of primary cortical receptive fields in terms of properties of the visual environment. Canonical correlation analysis explains similarly chromatic adaptation to different illuminations. But, as we show in this paper, neither of the two methods generalizes well to explain both spatio-chromatic processing and adaptation at the same time. We propose a statistical method which combines the desirable properties of independent component and canonical correlation analysis: It finds independent components in each data set which, across the two data sets, are related to each other via linear or higher-order correlations. The new method is as widely applicable as canonical correlation analysis, and also to more than two data sets. We call it higher-order canonical correlation analysis. When applied to chromatic natural images, we found that it provides a single (unified) statistical framework which accounts for both spatio-chromatic processing and adaptation. Filters with spatio-chromatic tuning properties as in the primary visual cortex emerged and corresponding-colors psychophysics was reproduced reasonably well. We used the new method to make a theory-driven testable prediction on how the neural response to colored patterns should change when the illumination changes. We predict shifts in the responses which are comparable to the shifts reported for chromatic contrast habituation.

Classification using sparse representations: a biologically plausible approach

Representing signals as linear combinations of basis vectors sparsely selected from an overcomplete dictionary has proven to be advantageous for many applications in pattern recognition, machine learning, signal processing, and computer vision. While this approach was originally inspired by insights into cortical information processing, biologically plausible approaches have been limited to exploring the functionality of early sensory processing in the brain, while more practical applications have employed non-biologically plausible sparse coding algorithms. Here, a biologically plausible algorithm is proposed that can be applied to practical problems. This algorithm is evaluated using standard benchmark tasks in the domain of pattern classification, and its performance is compared to a wide range of alternative algorithms that are widely used in signal and image processing. The results show that for the classification tasks performed here, the proposed method is competitive with the best of the alternative algorithms that have been evaluated. This demonstrates that classification using sparse representations can be performed in a neurally plausible manner, and hence, that this mechanism of classification might be exploited by the brain.

Phase synchrony facilitates binding and segmentation of natural images in a coupled neural oscillator network

Synchronization has been suggested as a mechanism of binding distributed feature representations facilitating segmentation of visual stimuli. Here we investigate this concept based on unsupervised learning using natural visual stimuli. We simulate dual-variable neural oscillators with separate activation and phase variables. The binding of a set of neurons is coded by synchronized phase variables. The network of tangential synchronizing connections learned from the induced activations exhibits small-world properties and allows binding even over larger distances. We evaluate the resulting dynamic phase maps using segmentation masks labeled by human experts. Our simulation results show a continuously increasing phase synchrony between neurons within the labeled segmentation masks. The evaluation of the network dynamics shows that the synchrony between network nodes establishes a relational coding of the natural image inputs. This demonstrates that the concept of binding by synchrony is applicable in the context of unsupervised learning using natural visual stimuli.

Sparse coding models can exhibit decreasing sparseness while learning sparse codes for natural images

The sparse coding hypothesis has enjoyed much success in predicting response properties of simple cells in primary visual cortex (V1) based solely on the statistics of natural scenes. In typical sparse coding models, model neuron activities and receptive fields are optimized to accurately represent input stimuli using the least amount of neural activity. As these networks develop to represent a given class of stimulus, the receptive fields are refined so that they capture the most important stimulus features. Intuitively, this is expected to result in sparser network activity over time. Recent experiments, however, show that stimulus-evoked activity in ferret V1 becomes less sparse during development, presenting an apparent challenge to the sparse coding hypothesis. Here we demonstrate that some sparse coding models, such as those employing homeostatic mechanisms on neural firing rates, can exhibit decreasing sparseness during learning, while still achieving good agreement with mature V1 receptive field shapes and a reasonably sparse mature network state. We conclude that observed developmental trends do not rule out sparseness as a principle of neural coding per se: a mature network can perform sparse coding even if sparseness decreases somewhat during development. To make comparisons between model and physiological receptive fields, we introduce a new nonparametric method for comparing receptive field shapes using image registration techniques.

Visual nonclassical receptive field effects emerge from sparse coding in a dynamical system

Extensive electrophysiology studies have shown that many V1 simple cells have nonlinear response properties to stimuli within their classical receptive field (CRF) and receive contextual influence from stimuli outside the CRF modulating the cell's response. Models seeking to explain these non-classical receptive field (nCRF) effects in terms of circuit mechanisms, input-output descriptions, or individual visual tasks provide limited insight into the functional significance of these response properties, because they do not connect the full range of nCRF effects to optimal sensory coding strategies. The (population) sparse coding hypothesis conjectures an optimal sensory coding approach where a neural population uses as few active units as possible to represent a stimulus. We demonstrate that a wide variety of nCRF effects are emergent properties of a single sparse coding model implemented in a neurally plausible network structure (requiring no parameter tuning to produce different effects). Specifically, we replicate a wide variety of nCRF electrophysiology experiments (e.g., end-stopping, surround suppression, contrast invariance of orientation tuning, cross-orientation suppression, etc.) on a dynamical system implementing sparse coding, showing that this model produces individual units that reproduce the canonical nCRF effects. Furthermore, when the population diversity of an nCRF effect has also been reported in the literature, we show that this model produces many of the same population characteristics. These results show that the sparse coding hypothesis, when coupled with a biophysically plausible implementation, can provide a unified high-level functional interpretation to many response properties that have generally been viewed through distinct mechanistic or phenomenological models.

Simple cells in the primary visual cortex (V1) demonstrate many response properties that are either nonlinear or involve response modulations (i.e., stimuli that do not cause a response in isolation alter the cell's response to other stimuli). These non-classical receptive field (nCRF) effects are generally modeled individually and their collective role in biological vision is not well understood. Previous work has shown that classical receptive field (CRF) properties of V1 cells (i.e., the spatial structure of the visual field responsive to stimuli) could be explained by the sparse coding hypothesis, which is an optimal coding model that conjectures a neural population should use the fewest number of cells simultaneously to represent each stimulus. In this paper, we have performed extensive simulated physiology experiments to show that many nCRF response properties are simply emergent effects of a dynamical system implementing this same sparse coding model. These results suggest that rather than representing disparate information processing operations themselves, these nCRF effects could be consequences of an optimal sensory coding strategy that attempts to represent each stimulus most efficiently. This interpretation provides a potentially unifying high-level functional interpretation to many response properties that have generally been viewed through distinct models.

Are v1 simple cells optimized for visual occlusions? A comparative study

Simple cells in primary visual cortex were famously found to respond to low-level image components such as edges. Sparse coding and independent component analysis (ICA) emerged as the standard computational models for simple cell coding because they linked their receptive fields to the statistics of visual stimuli. However, a salient feature of image statistics, occlusions of image components, is not considered by these models. Here we ask if occlusions have an effect on the predicted shapes of simple cell receptive fields. We use a comparative approach to answer this question and investigate two models for simple cells: a standard linear model and an occlusive model. For both models we simultaneously estimate optimal receptive fields, sparsity and stimulus noise. The two models are identical except for their component superposition assumption. We find the image encoding and receptive fields predicted by the models to differ significantly. While both models predict many Gabor-like fields, the occlusive model predicts a much sparser encoding and high percentages of 'globular' receptive fields. This relatively new center-surround type of simple cell response is observed since reverse correlation is used in experimental studies. While high percentages of 'globular' fields can be obtained using specific choices of sparsity and overcompleteness in linear sparse coding, no or only low proportions are reported in the vast majority of studies on linear models (including all ICA models). Likewise, for the here investigated linear model and optimal sparsity, only low proportions of 'globular' fields are observed. In comparison, the occlusive model robustly infers high proportions and can match the experimentally observed high proportions of 'globular' fields well. Our computational study, therefore, suggests that 'globular' fields may be evidence for an optimal encoding of visual occlusions in primary visual cortex.

Inhibitory interneurons decorrelate excitatory cells to drive sparse code formation in a spiking model of V1

Sparse coding models of natural scenes can account for several physiological properties of primary visual cortex (V1), including the shapes of simple cell receptive fields (RFs) and the highly kurtotic firing rates of V1 neurons. Current spiking network models of pattern learning and sparse coding require direct inhibitory connections between the excitatory simple cells, in conflict with the physiological distinction between excitatory (glutamatergic) and inhibitory (GABAergic) neurons (Dale's Law). At the same time, the computational role of inhibitory neurons in cortical microcircuit function has yet to be fully explained. Here we show that adding a separate population of inhibitory neurons to a spiking model of V1 provides conformance to Dale's Law, proposes a computational role for at least one class of interneurons, and accounts for certain observed physiological properties in V1. When trained on natural images, this excitatory-inhibitory spiking circuit learns a sparse code with Gabor-like RFs as found in V1 using only local synaptic plasticity rules. The inhibitory neurons enable sparse code formation by suppressing predictable spikes, which actively decorrelates the excitatory population. The model predicts that only a small number of inhibitory cells is required relative to excitatory cells and that excitatory and inhibitory input should be correlated, in agreement with experimental findings in visual cortex. We also introduce a novel local learning rule that measures stimulus-dependent correlations between neurons to support "explaining away" mechanisms in neural coding.

Sparse coding can predict primary visual cortex receptive field changes induced by abnormal visual input

Receptive fields acquired through unsupervised learning of sparse representations of natural scenes have similar properties to primary visual cortex (V1) simple cell receptive fields. However, what drives in vivo development of receptive fields remains controversial. The strongest evidence for the importance of sensory experience in visual development comes from receptive field changes in animals reared with abnormal visual input. However, most sparse coding accounts have considered only normal visual input and the development of monocular receptive fields. Here, we applied three sparse coding models to binocular receptive field development across six abnormal rearing conditions. In every condition, the changes in receptive field properties previously observed experimentally were matched to a similar and highly faithful degree by all the models, suggesting that early sensory development can indeed be understood in terms of an impetus towards sparsity. As previously predicted in the literature, we found that asymmetries in inter-ocular correlation across orientations lead to orientation-specific binocular receptive fields. Finally we used our models to design a novel stimulus that, if present during rearing, is predicted by the sparsity principle to lead robustly to radically abnormal receptive fields.

The responses of neurons in the primary visual cortex (V1), a region of the brain involved in encoding visual input, are modified by the visual experience of the animal during development. For example, most neurons in animals reared viewing stripes of a particular orientation only respond to the orientation that the animal experienced. The responses of V1 cells in normal animals are similar to responses that simple optimisation algorithms can learn when trained on images. However, whether the similarity between these algorithms and V1 responses is merely coincidental has been unclear. Here, we used the results of a number of experiments where animals were reared with modified visual experience to test the explanatory power of three related optimisation algorithms. We did this by filtering the images for the algorithms in ways that mimicked the visual experience of the animals. This allowed us to show that the changes in V1 responses in experiment were consistent with the algorithms. This is evidence that the precepts of the algorithms, notably sparsity, can be used to understand the development of V1 responses. Further, we used our model to propose a novel rearing condition which we expect to have a dramatic effect on development.

Perceptual decision making "through the eyes" of a large-scale neural model of v1

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.