If modern computers are sometimes superior to humans in some specialized tasks such as playing chess or browsing a large database, they can't beat the efficiency of biological vision for such simple tasks as recognizing and following an object in a complex cluttered background. We present in this paper our attempt at outlining the dynamical, parallel and event-based representation for vision in the architecture of the central nervous system. We will illustrate this on static natural images by showing that in a signal matching framework, a L/LN (linear/non-linear) cascade may efficiently transform a sensory signal into a neural spiking signal and we will apply this framework to a model retina. However, this code gets redundant when using an over-complete basis as is necessary for modeling the primary visual cortex: we therefore optimize the efficiency cost by increasing the sparseness of the code. This is implemented by propagating and canceling redundant information using lateral interactions. We compare the efficiency of this representation in terms of compression as the reconstruction quality as a function of the coding length. This will correspond to a modification of the Matching Pursuit algorithm where the ArgMax function is optimized for competition, or Competition Optimized Matching Pursuit (COMP). We will in particular focus on bridging neuroscience and image processing and on the advantages of such an interdisciplinary approach.
Over the last decade several positive definite kernels have been proposed to treat spike trains as objects in Hilbert space. However, for the most part, such attempts still remain a mere curiosity for both computational neuroscientists and signal processing experts. This tutorial illustrates why kernel methods can, and have already started to, change the way spike trains are analyzed and processed. The presentation incorporates simple mathematical analogies and convincing practical examples in an attempt to show the yet unexplored potential of positive definite functions to quantify point proc…
Sparse coding networks, which utilize unsupervised learning to maximize coding efficiency, have successfully reproduced response properties found in primary visual cortex \cite{AN:OlshausenField96}. However, conventional sparse coding models require that the coding circuit can fully sample the sensory data in a one-to-one fashion, a requirement not supported by experimental data from the thalamo-cortical projection. To relieve these strict wiring requirements, we propose a sparse coding network constructed by introducing synaptic learning in the framework of compressed sensing. We demonstrate …
Latency reduction of postsynaptic spikes is a well-known effect of Synaptic Time-Dependent Plasticity. We expand this notion for long postsynaptic spike trains, showing that, for a fixed input spike train, STDP reduces the number of postsynaptic spikes and concentrates the remaining ones. Then we study the consequences of this phenomena in terms of coding, finding that this mechanism improves the neural code by increasing the signal-to-noise ratio and lowering the metabolic costs of frequent stimuli. Finally, we illustrate that the reduction of postsynaptic latencies can lead to the emergence …
Background: It is commonly assumed in neuronal coding that repeated presentations of a stimulus to a coding neuron elicit similar responses. One common way to assess similarity are spike train distances. These can be divided into spike-resolved, such as the Victor-Purpura and the van Rossum distance, and time-resolved, e.g. the ISI-, the SPIKE- and the RI-SPIKE-distance. New Method: We use independent steady-rate Poisson processes as surrogates for spike trains with fixed rate and no timing information to address two basic questions: How does the sensitivity of the different spike train distan…
In many animal sensory pathways, the transformation from external stimuli to spike trains is essentially deterministic. In this context, a new mathematical framework for coding and reconstruction, based on a biologically plausible model of the spiking neuron, is presented. The framework considers encoding of a signal through spike trains generated by an ensemble of neurons via a standard convolve-then-threshold mechanism. Neurons are distinguished by their convolution kernels and threshold values. Reconstruction is posited as a convex optimization minimizing energy. Formal conditions under whi…
We would like to know whether the statistics of neuronal responses vary across cortical areas. We examined stimulus-elicited spike count response distributions in V1 and IT cortices of awake monkeys. In both areas the distribution of spike counts for each stimulus was well-described by a Gaussian, with the log of the variance in the spike count linearly related to the log of the mean spike count. Two significant differences in response characteristics were found: both the range of spike counts and the slope of the log(variance) vs. log(mean) regression were larger in V1 than in IT. However, ne…
Repetitive spatio-temporal propagation patterns are encountered in fields as wide-ranging as climatology, social communication and network science. In neuroscience, perfectly consistent repetitions of the same global propagation pattern are called a synfire pattern. For any recording of sequences of discrete events (in neuroscience terminology: sets of spike trains) the questions arise how closely it resembles such a synfire pattern and which are the spike trains that lead/follow. Here we address these questions and introduce an algorithm built on two new indicators, termed SPIKE-Order and Spi…
We study the reconstruction of visual stimuli from spike trains, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. If the reconstructed stimulus is to be represented by a Volterra series and correlations between spikes are to be taken into account, first order expansions are insufficient and we have to go to second order, at least. In this case higher order correlation functions have to be manipulated, whose size may become prohibitively …
The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle corresponding, in its simplest form, to the Maximum Entropy principle. It is used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science. In particular, it has been fruitful and influential in neurosciences. In this article, we review how the Thermodynam…
Information processing in the brain crucially depends on encoding properties of single neurons, with particular relevance of the spike-generation mechanism. The latter hinges upon the bifurcation type at the transition point between resting state and limit cycle spiking. Prominent qualitative changes in encoding have previously been attributed to a specific switch of such a bifurcation at the Bogdanov-Takens (BT) point. This study unveils another, highly relevant and so far underestimated transition point: the saddle-node loop bifurcation. As we show, this bifurcation turns out to induce even …
Neurons in the nervous system convey information to higher brain regions by the generation of spike trains. An important question in the field of computational neuroscience is how these sensory neurons encode environmental information in a way which may be simply analyzed by subsequent systems. Many aspects of the form and function of the nervous system have been understood using the concepts of optimal population coding. Most studies, however, have neglected the aspect of temporal coding. Here we address this shortcoming through a filtering theory of inhomogeneous Poisson processes. We derive…
We demonstrate that the information contained in the spike occurrence times of a population of neurons can be broken up into a series of terms, each of which reflect something about potential coding mechanisms. This is possible in the coding r{é}gime in which few spikes are emitted in the relevant time window. This approach allows us to study the additional information contributed by spike timing beyond that present in the spike counts; to examine the contributions to the whole information of different statistical properties of spike trains, such as firing rates and correlation functions; and …
Spiking Neural Networks (SNNs) have shown great potential in solving deep learning problems in an energy-efficient manner. However, they are still limited to simple classification tasks. In this paper, we propose Spiking-GAN, the first spike-based Generative Adversarial Network (GAN). It employs a kind of temporal coding scheme called time-to-first-spike coding. We train it using approximate backpropagation in the temporal domain. We use simple integrate-and-fire (IF) neurons with very high refractory period for our network which ensures a maximum of one spike per neuron. This makes the model …
The role of synchronous firing in sensory coding and cognition remains controversial. While studies, focusing on its mechanistic consequences in attentional tasks, suggest that synchronization dynamically boosts sensory processing, others failed to find significant synchronization levels in such tasks. We attempt to understand both lines of evidence within a coherent theoretical framework. We conceptualize synchronization as an independent control parameter to study how the postsynaptic neuron transmits the average firing activity of a presynaptic population, in the presence of synchronization…
A key question in neuroscience is at which level functional meaning emerges from biophysical phenomena. In most vertebrate systems, precise functions are assigned at the level of neural populations, while single-neurons are deemed unreliable and redundant. Here we challenge this view and show that many single-neuron quantities, including voltages, firing thresholds, excitation, inhibition, and spikes, acquire precise functional meaning whenever a network learns to transmit information parsimoniously and precisely to the next layer. Based on the hypothesis that neural circuits generate precise …
To understand possible strategies of temporal spike coding in the central nervous system, we study functional neuromimetic models of visual processing for static images. We will first present the retinal model which was introduced by Van Rullen and Thorpe and which represents the multiscale contrast values of the image using an orthonormal wavelet transform. These analog values activate a set of spiking neurons which each fire once to produce an asynchronous wave of spikes. According to this model, the image may be progressively reconstructed from this spike wave thanks to regularities in the …
Definition. The phase-of-firing code is a neural coding scheme whereby neurons encode information using the time at which they fire spikes within a cycle of the ongoing oscillatory pattern of network activity. This coding scheme may allow neurons to use their temporal pattern of spikes to encode information that is not encoded in their firing rate.
Rochester Institute of Technology（罗切斯特理工学院）；AI Research Lab（AI研究实验室）；University of Washington（华盛顿大学）；Rochester, New York, USA（纽约罗切斯特市）；Los Angeles, California, USA（加州洛杉矶市）；Seattle, Washington, USA（华盛顿州西雅图市）
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）；Columbia University（哥伦比亚大学）
Decoding behavior, perception, or cognitive state directly from neural signals has applications in brain-computer interface research as well as implications for systems neuroscience. In the last decade, deep learning has become the state-of-the-art method in many machine learning tasks ranging from speech recognition to image segmentation. The success of deep networks in other domains has led to a new wave of applications in neuroscience. In this article, we review deep learning approaches to neural decoding. We describe the architectures used for extracting useful features from neural recordi…
In nature, animals encounter high dimensional sensory stimuli that have complex statistical and dynamical structure. Attempts to study the neural coding of these natural signals face challenges both in the selection of the signal ensemble and in the analysis of the resulting neural responses. For zebra finches, naturalistic stimuli can be defined as sounds that they encounter in a colony of conspecific birds. We assembled an ensemble of these sounds by recording groups of 10-40 zebra finches, and then analyzed the response of single neurons in the songbird central auditory area (field L) to co…
Linear Non-Linear(LN) models are widely used to characterize the receptive fields of early-stage auditory processing. We apply the principle of efficient coding to the LN model of Spectro-Temporal Receptive Fields(STRFs) of the neurons in primary auditory cortex. The Efficient Coding Principle has been previously used to understand early visual receptive fields and linear STRFs in auditory processing. Efficient coding is realized by jointly optimizing the mutual information between stimuli and neural responses subjected to the metabolic cost of firing spikes. We compare the predictions of the …
Here is proposed a review of the different choices to structure spike trains, using deterministic metrics. Temporal constraints observed in biological or computational spike trains are first taken into account. The relation with existing neural codes (rate coding, rank coding, phase coding, ..) is then discussed. To which extend the "neural code" contained in spike trains is related to a metric appears to be a key point, a generalization of the Victor-Purpura metric family being proposed for temporal constrained causal spike trains
In terms of the long-distance communication of a single neuron, interpulse intervals (IPIs) are a possible alternative to rate and binary codes. As a proxy for IPI, the time-to-spike (TTS) for a neuron can be found in the biophysical and experimental literature. Using the current, consensus layer V pyramidal neuron, the present study examines the feasibility of IPI-coding and examines the noise sources that limit the information rate of such an encoding. In descending order of noise intensity, the noise sources are (i) synaptic variability, (ii) sodium channel shot-noise, followed by (iii) the…
Neural coding is a field of study that concerns how sensory information is represented in the brain by networks of neurons. The link between external stimulus and neural response can be studied from two parallel points of view. The first, neural encoding refers to the mapping from stimulus to response, and primarily focuses on understanding how neurons respond to a wide variety of stimuli, and on constructing models that accurately describe the stimulus-response relationship. Neural decoding, on the other hand, refers to the reverse mapping, from response to stimulus, where the challenge is to…
The hippocampal system contains neural populations that encode an animal's position and velocity as it navigates through space. Here, we show that such populations can embed two codes within their spike trains: a firing rate code (R) conveyed by within-cell spike intervals, and a co-firing rate code (R') conveyed by between-cell spike intervals. These two codes behave as conjugates of one another, obeying an analog of the uncertainty principle from physics: information conveyed in R comes at the expense of information in R', and vice versa. An exception to this trade-off occurs when spike trai…
A steadily increasing body of evidence suggests that the brain performs probabilistic inference to interpret and respond to sensory input and that trial-to-trial variability in neural activity plays an important role. The neural sampling hypothesis interprets stochastic neural activity as sampling from an underlying probability distribution and has been shown to be compatible with biologically observed firing patterns. In many studies, uncorrelated noise is used as a source of stochasticity, discounting the fact that cortical neurons may share a significant portion of their presynaptic partner…
Our knowledge of the sensory world is encoded by neurons in sequences of discrete, identical pulses termed action potentials or spikes. There is persistent controversy about the extent to which the precise timing of these spikes is relevant to the function of the brain. We revisit this issue, using the motion-sensitive neurons of the fly visual system as a test case. New experimental methods allow us to deliver more nearly natural visual stimuli, comparable to those which flies encounter in free, acrobatic flight, and new mathematical methods allow us to draw more reliable conclusions about th…
Understanding how the dynamics of neural networks is shaped by the computations they perform is a fundamental question in neuroscience. Recently, the framework of efficient coding proposed a theory of how spiking neural networks can compute low-dimensional stimulus signals with high efficiency. Efficient spiking networks are based on time-dependent minimization of a loss function related to information coding with spikes. To inform the understanding of the function and dynamics of biological networks in the brain, however, the mathematical models have to be informed by biology and obey the sam…
The timing of individual neuronal spikes is essential for biological brains to make fast responses to sensory stimuli. However, conventional artificial neural networks lack the intrinsic temporal coding ability present in biological networks. We propose a spiking neural network model that encodes information in the relative timing of individual neuron spikes. In classification tasks, the output of the network is indicated by the first neuron to spike in the output layer. This temporal coding scheme allows the supervised training of the network with backpropagation, using locally exact derivati…
Knowledge about the collective dynamics of cortical spiking is very informative about the underlying coding principles. However, even most basic properties are not known with certainty, because their assessment is hampered by spatial subsampling, i.e. the limitation that only a tiny fraction of all neurons can be recorded simultaneously with millisecond precision. Building on a novel, subsampling-invariant estimator, we fit and carefully validate a minimal model for cortical spike propagation. The model interpolates between two prominent states: asynchronous and critical. We find neither of th…
Statistical analysis and inference on spike trains is one of the central topics in the neural coding. It is of great interest to understand the underlying structure of given neural data. Based on the metric distances between spike trains, recent investigations have introduced the notion of an average or prototype spike train to characterize the template pattern in the neural activity. However, as those metrics lack certain Euclidean properties, the defined averages are nonunique, and do not share the conventional properties of a mean. In this article, we propose a new framework to define the m…
The relationship between a neuron's complex inputs and its spiking output defines the neuron's coding strategy. This is frequently and effectively modeled phenomenologically by one or more linear filters that extract the components of the stimulus that are relevant for triggering spikes, and a nonlinear function that relates stimulus to firing probability. In many sensory systems, these two components of the coding strategy are found to adapt to changes in the statistics of the inputs, in such a way as to improve information transmission. Here, we show for two simple neuron models how feature …
Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising recent work utilized a convolutive nonnegative matrix factorization model to tackle this challenge. However, this model requires spike times to be discretized, utilizes a sub-optimal least-squares criterion, and does not provide uncertainty estimates for model predictions or estimated parameters. We address each of these shortcomings by developing a point proces…
The problem of neural coding is to understand how sequences of action potentials (spikes) are related to sensory stimuli, motor outputs, or (ultimately) thoughts and intentions. One clear question is whether the same coding rules are used by different neurons, or by corresponding neurons in different individuals. We present a quantitative formulation of this problem using ideas from information theory, and apply this approach to the analysis of experiments in the fly visual system. We find significant individual differences in the structure of the code, particularly in the way that temporal pa…
Optogenetics is an emerging field of neuroscience where neurons are genetically modified to express light-sensitive receptors that enable external control over when the neurons fire. Given the prominence of neuronal signaling within the brain and throughout the body, optogenetics has significant potential to improve the understanding of the nervous system and to develop treatments for neurological diseases. This paper uses a simple optogenetic model to compare the timing distortion between a randomly-generated target spike sequence and an externally-stimulated neuron spike sequence. The distor…
We propose a new supervised learning rule for multilayer spiking neural networks (SNNs) that use a form of temporal coding known as rank-order-coding. With this coding scheme, all neurons fire exactly one spike per stimulus, but the firing order carries information. In particular, in the readout layer, the first neuron to fire determines the class of the stimulus. We derive a new learning rule for this sort of network, named S4NN, akin to traditional error backpropagation, yet based on latencies. We show how approximated error gradients can be computed backward in a feedforward network with an…
It has long been debated whether information in the brain is coded at the rate of neuronal spiking or at the precise timing of single spikes. Although this issue is essential to the understanding of neural signal processing, it is not easily resolved because the two mechanisms are not mutually exclusive. We suggest revising this coding issue so that one hypothesis is uniquely selected for a given spike train. To this end, we decide whether the spike train is likely to transmit a continuously varying analog signal or switching between active and inactive states. The coding hypothesis is selecte…
This paper uses a simple optogenetic model to compare the timing distortion between a randomly-generated target spike sequence and an externally-stimulated neuron spike sequence. Optogenetics is an emerging field of neuroscience where neurons are genetically modified to express light-sensitive receptors that enable external control over when the neurons fire. Given the prominence of neuronal signaling within the brain and throughout the body, optogenetics has significant potential to improve the understanding of the nervous system and to develop treatments for neurological diseases. This paper…
In this article, our wish is to demystify some aspects of coding with spike-timing, through a simple review of well-understood technical facts regarding spike coding. The goal is to help better understanding to which extend computing and modelling with spiking neuron networks can be biologically plausible and computationally efficient. We intentionally restrict ourselves to a deterministic dynamics, in this review, and we consider that the dynamics of the network is defined by a non-stochastic mapping. This allows us to stay in a rather simple framework and to propose a review with concrete nu…
The spiking neural networks (SNNs) are considered as one of the most promising artificial neural networks due to their energy efficient computing capability. Recently, conversion of a trained deep neural network to an SNN has improved the accuracy of deep SNNs. However, most of the previous studies have not achieved satisfactory results in terms of inference speed and energy efficiency. In this paper, we propose a fast and energy-efficient information transmission method with burst spikes and hybrid neural coding scheme in deep SNNs. Our experimental results showed the proposed methods can imp…
A main concern in cognitive neuroscience is to decode the overt neural spike train observations and infer latent representations under neural circuits. However, traditional methods entail strong prior on network structure and hardly meet the demand for real spike data. Here we propose a novel neural network approach called Neuron Activation Network that extracts neural information explicitly from single trial neuron population spike trains. Our proposed method consists of a spatiotemporal learning procedure on sensory environment and a message passing mechanism on population graph, followed by…
National Engineering Laboratory for Video Technology, School of Electronics Engineering and Computer Science, Peking University（北京大学电子信息工程学院视频技术国家工程实验室）；Peng Cheng Laboratory（鹏城实验室）；Centre for Systems Neuroscience, Department of Neuroscience, Psychology and Behaviour, University of Leicester（莱斯特大学神经科学、心理学与行为学系系统神经科学中心）
Neural coding is one of the central questions in systems neuroscience for understanding how the brain processes stimulus from the environment, moreover, it is also a cornerstone for designing algorithms of brain-machine interface, where decoding incoming stimulus is highly demanded for better performance of physical devices. Traditionally researchers have focused on functional magnetic resonance imaging (fMRI) data as the neural signals of interest for decoding visual scenes. However, our visual perception operates in a fast time scale of millisecond in terms of an event termed neural spike. T…
Directorate of Technology and Innovation（技术与创新局）；Chamber of Deputies（众议院）
Deep predictive coding networks are neuroscience-inspired unsupervised learning models that learn to predict future sensory states. We build upon the PredNet implementation by Lotter, Kreiman, and Cox (2016) to investigate if predictive coding representations are useful to predict brain activity in the visual cortex. We use representational similarity analysis (RSA) to compare PredNet representations to functional magnetic resonance imaging (fMRI) and magnetoencephalography (MEG) data from the Algonauts Project. In contrast to previous findings in the literature (Khaligh-Razavi &Kriegeskorte, …
