Role of homeostasis in learning sparse representations

A robust event-driven approach to always-on object recognition

We propose a neuromimetic architecture capable of always-on pattern recognition, i.e. at any time during processing. To achieve this, we have extended an existing event-based algorithm (Lagorce et al., 2017), which introduced novel spatio-temporal features as a Hierarchy Of Time-Surfaces (HOTS). Built from asynchronous events captured by a neuromorphic camera, these time surfaces allow to encode the local dynamics of a visual scene and to create an efficient event-based pattern recognition architecture. Inspired by neuroscience, we have extended this method to improve its performance. First, we add a homeostatic gain control on the activity of neurons to improve the learning of spatio-temporal patterns (Grimaldi et al., 2021). We also provide a new mathematical formalism that allows an analogy to be drawn between the HOTS algorithm and Spiking Neural Networks (SNN). Following this analogy, we transform the offline pattern categorization method into an online and event-driven layer. This classifier uses the spiking output of the network to define new time surfaces and we then perform the online classification with a neuromimetic implementation of a multinomial logistic regression. These improvements not only consistently increase the performance of the network, but also bring this event-driven pattern recognition algorithm fully online. The results have been validated on different datasets: Poker-DVS (Serrano-Gotarredona and Linares-Barranco, 2015), N-MNIST (Orchard, Jayawant et al., 2015) and DVS Gesture (Amir et al., 2017). This demonstrates the efficiency of this bio-realistic SNN for ultra-fast object recognition through an event-by-event categorization process.

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.

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.

The HTM Spatial Pooler-A Neocortical Algorithm for Online Sparse Distributed Coding

Hierarchical temporal memory (HTM) provides a theoretical framework that models several key computational principles of the neocortex. In this paper, we analyze an important component of HTM, the HTM spatial pooler (SP). The SP models how neurons learn feedforward connections and form efficient representations of the input. It converts arbitrary binary input patterns into sparse distributed representations (SDRs) using a combination of competitive Hebbian learning rules and homeostatic excitability control. We describe a number of key properties of the SP, including fast adaptation to changing input statistics, improved noise robustness through learning, efficient use of cells, and robustness to cell death. In order to quantify these properties we develop a set of metrics that can be directly computed from the SP outputs. We show how the properties are met using these metrics and targeted artificial simulations. We then demonstrate the value of the SP in a complete end-to-end real-world HTM system. We discuss the relationship with neuroscience and previous studies of sparse coding. The HTM spatial pooler represents a neurally inspired algorithm for learning sparse representations from noisy data streams in an online fashion.

Role of the site of synaptic competition and the balance of learning forces for Hebbian encoding of probabilistic Markov sequences

The majority of distinct sensory and motor events occur as temporally ordered sequences with rich probabilistic structure. Sequences can be characterized by the probability of transitioning from the current state to upcoming states (forward probability), as well as the probability of having transitioned to the current state from previous states (backward probability). Despite the prevalence of probabilistic sequencing of both sensory and motor events, the Hebbian mechanisms that mold synapses to reflect the statistics of experienced probabilistic sequences are not well understood. Here, we show through analytic calculations and numerical simulations that Hebbian plasticity (correlation, covariance, and STDP) with pre-synaptic competition can develop synaptic weights equal to the conditional forward transition probabilities present in the input sequence. In contrast, post-synaptic competition can develop synaptic weights proportional to the conditional backward probabilities of the same input sequence. We demonstrate that to stably reflect the conditional probability of a neuron's inputs and outputs, local Hebbian plasticity requires balance between competitive learning forces that promote synaptic differentiation and homogenizing learning forces that promote synaptic stabilization. The balance between these forces dictates a prior over the distribution of learned synaptic weights, strongly influencing both the rate at which structure emerges and the entropy of the final distribution of synaptic weights. Together, these results demonstrate a simple correspondence between the biophysical organization of neurons, the site of synaptic competition, and the temporal flow of information encoded in synaptic weights by Hebbian plasticity while highlighting the utility of balancing learning forces to accurately encode probability distributions, and prior expectations over such probability distributions.

Stability of Neuronal Networks with Homeostatic Regulation

Neurons are equipped with homeostatic mechanisms that counteract long-term perturbations of their average activity and thereby keep neurons in a healthy and information-rich operating regime. While homeostasis is believed to be crucial for neural function, a systematic analysis of homeostatic control has largely been lacking. The analysis presented here analyses the necessary conditions for stable homeostatic control. We consider networks of neurons with homeostasis and show that homeostatic control that is stable for single neurons, can destabilize activity in otherwise stable recurrent networks leading to strong non-abating oscillations in the activity. This instability can be prevented by slowing down the homeostatic control. The stronger the network recurrence, the slower the homeostasis has to be. Next, we consider how non-linearities in the neural activation function affect these constraints. Finally, we consider the case that homeostatic feedback is mediated via a cascade of multiple intermediate stages. Counter-intuitively, the addition of extra stages in the homeostatic control loop further destabilizes activity in single neurons and networks. Our theoretical framework for homeostasis thus reveals previously unconsidered constraints on homeostasis in biological networks, and identifies conditions that require the slow time-constants of homeostatic regulation observed experimentally.

Despite their apparent robustness many biological system work best in controlled environments, the tightly regulated mammalian body temperature being a good example. Biological homeostatic control systems, not unlike those used in engineering, ensure that the right operating conditions are met. Similarly, neurons appear to adjust the amount of activity they produce to be neither too high nor too low by, among other ways, regulating their excitability. However, for no apparent reason the neural homeostatic processes are very slow, taking hours or even days to regulate the neuron. Here we use results from mathematical control theory to examine under which conditions such slow control is necessary to prevent instabilities that lead to strong, sustained oscillations in the activity. Our results lead to a deeper understanding of neural homeostasis and can help the design of artificial neural systems.

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.

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.

Invariant scattering convolution networks

A wavelet scattering network computes a translation invariant image representation which is stable to deformations and preserves high-frequency information for classification. It cascades wavelet transform convolutions with nonlinear modulus and averaging operators. The first network layer outputs SIFT-type descriptors, whereas the next layers provide complementary invariant information that improves classification. The mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification. A scattering representation of stationary processes incorporates higher order moments and can thus discriminate textures having the same Fourier power spectrum. State-of-the-art classification results are obtained for handwritten digits and texture discrimination, with a Gaussian kernel SVM and a generative PCA classifier.

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.

Image segmentation using a sparse coding model of cortical area V1

Algorithms that encode images using a sparse set of basis functions have previously been shown to explain aspects of the physiology of a primary visual cortex (V1), and have been used for applications, such as image compression, restoration, and classification. Here, a sparse coding algorithm, that has previously been used to account for the response properties of orientation tuned cells in primary visual cortex, is applied to the task of perceptually salient boundary detection. The proposed algorithm is currently limited to using only intensity information at a single scale. However, it is shown to out-perform the current state-of-the-art image segmentation method (Pb) when this method is also restricted to using the same information.

Motion-based prediction is sufficient to solve the aperture problem

In low-level sensory systems, it is still unclear how the noisy information collected locally by neurons may give rise to a coherent global percept. This is well demonstrated for the detection of motion in the aperture problem: as luminance of an elongated line is symmetrical along its axis, tangential velocity is ambiguous when measured locally. Here, we develop the hypothesis that motion-based predictive coding is sufficient to infer global motion. Our implementation is based on a context-dependent diffusion of a probabilistic representation of motion. We observe in simulations a progressive solution to the aperture problem similar to physiology and behavior. We demonstrate that this solution is the result of two underlying mechanisms. First, we demonstrate the formation of a tracking behavior favoring temporally coherent features independent of their texture. Second, we observe that incoherent features are explained away, while coherent information diffuses progressively to the global scale. Most previous models included ad hoc mechanisms such as end-stopped cells or a selection layer to track specific luminance-based features as necessary conditions to solve the aperture problem. Here, we have proved that motion-based predictive coding, as it is implemented in this functional model, is sufficient to solve the aperture problem. This solution may give insights into the role of prediction underlying a large class of sensory computations.

Compressed sensing, sparsity, and dimensionality in neuronal information processing and data analysis

The curse of dimensionality poses severe challenges to both technical and conceptual progress in neuroscience. In particular, it plagues our ability to acquire, process, and model high-dimensional data sets. Moreover, neural systems must cope with the challenge of processing data in high dimensions to learn and operate successfully within a complex world. We review recent mathematical advances that provide ways to combat dimensionality in specific situations. These advances shed light on two dual questions in neuroscience. First, how can we as neuroscientists rapidly acquire high-dimensional data from the brain and subsequently extract meaningful models from limited amounts of these data? And second, how do brains themselves process information in their intrinsically high-dimensional patterns of neural activity as well as learn meaningful, generalizable models of the external world from limited experience?

Motion clouds: model-based stimulus synthesis of natural-like random textures for the study of motion perception

Choosing an appropriate set of stimuli is essential to characterize the response of a sensory system to a particular functional dimension, such as the eye movement following the motion of a visual scene. Here, we describe a framework to generate random texture movies with controlled information content, i.e., Motion Clouds. These stimuli are defined using a generative model that is based on controlled experimental parametrization. We show that Motion Clouds correspond to dense mixing of localized moving gratings with random positions. Their global envelope is similar to natural-like stimulation with an approximate full-field translation corresponding to a retinal slip. We describe the construction of these stimuli mathematically and propose an open-source Python-based implementation. Examples of the use of this framework are shown. We also propose extensions to other modalities such as color vision, touch, and audition.

A sparse coding model with synaptically local plasticity and spiking neurons can account for the diverse shapes of V1 simple cell receptive fields

Sparse coding algorithms trained on natural images can accurately predict the features that excite visual cortical neurons, but it is not known whether such codes can be learned using biologically realistic plasticity rules. We have developed a biophysically motivated spiking network, relying solely on synaptically local information, that can predict the full diversity of V1 simple cell receptive field shapes when trained on natural images. This represents the first demonstration that sparse coding principles, operating within the constraints imposed by cortical architecture, can successfully reproduce these receptive fields. We further prove, mathematically, that sparseness and decorrelation are the key ingredients that allow for synaptically local plasticity rules to optimize a cooperative, linear generative image model formed by the neural representation. Finally, we discuss several interesting emergent properties of our network, with the intent of bridging the gap between theoretical and experimental studies of visual cortex.

In a sparse coding model, individual input stimuli are represented by the activities of model neurons, the majority of which are inactive in response to any particular stimulus. For a given class of stimuli, the neurons are optimized so that the stimuli can be faithfully represented with the minimum number of co-active units. This has been proposed as a model for visual cortex. While it has previously been demonstrated that sparse coding model neurons, when trained on natural images, learn to represent the same features as do neurons in primate visual cortex, it remains to be demonstrated that this can be achieved with physiologically realistic plasticity rules. In particular, learning in cortex appears to occur by the modification of synaptic connections between neurons, which must depend only on information available locally, at the synapse, and not, for example, on the properties of large numbers of distant cells. We provide the first demonstration that synaptically local plasticity rules are sufficient to learn a sparse image code, and to account for the observed response properties of visual cortical neurons: visual cortex actually could learn a sparse image code.

Unsupervised learning of generative and discriminative weights encoding elementary image components in a predictive coding model of cortical function

A method is presented for learning the reciprocal feedforward and feedback connections required by the predictive coding model of cortical function. When this method is used, feedforward and feedback connections are learned simultaneously and independently in a biologically plausible manner. The performance of the proposed algorithm is evaluated by applying it to learning the elementary components of artificial and natural images. For artificial images, the bars problem is employed, and the proposed algorithm is shown to produce state-of-the-art performance on this task. For natural images, components resembling Gabor functions are learned in the first processing stage, and neurons responsive to corners are learned in the second processing stage. The properties of these learned representations are in good agreement with neurophysiological data from V1 and V2. The proposed algorithm demonstrates for the first time that a single computational theory can explain the formation of cortical RFs and also the response properties of cortical neurons once those RFs have been learned.