Entropy-based parametric estimation of spike train statistics

We consider the evolution of a network of neurons, focusing on the asymptotic behavior of spikes dynamics instead of membrane potential dynamics. The spike response is not sought as a deterministic response in this context, but as a conditional probability : "Reading out the code" consists of inferring such a probability. This probability is computed from empirical raster plots, by using the framework of thermodynamic formalism in ergodic theory. This gives us a parametric statistical model where the probability has the form of a Gibbs distribution. In this respect, this approach generalizes the seminal and profound work of Schneidman and collaborators. A minimal presentation of the formalism is reviewed here, while a general algorithmic estimation method is proposed yielding fast convergent implementations. It is also made explicit how several spike observables (entropy, rate, synchronizations, correlations) are given in closed-form from the parametric estimation. This paradigm does not only allow us to estimate the spike statistics, given a design choice, but also to compare different models, thus answering comparative questions about the neural code such as : "are correlations (or time synchrony or a given set of spike patterns, ..) significant with respect to rate coding only ?" A numerical validation of the method is proposed and the perspectives regarding spike-train code analysis are also discussed.Comment: 37 pages, 8 figures, submitte

Biologically plausible regularization mechanisms

This study aims at proposing an implementation of regularization mechanisms compatible with biological operators. More precisely, cortical maps code vectorial parametric quantities, computed by network of neurons. In computer vision, similar quantities are efficiently computed using implementations of partial differential equations which define regularization processes allowing to obtain well-defined estimations of these quantities. One of these methods, introduced by Raviat and developed by Degond and Mas-Gallic, is based on an integral approximation of the diffusion operator used in regularization mechanisms. Following this formulation, the present development defines a somehow optimal implementation of such an integral operator with two interesting properties: (i) when used on sampled data such as image pixels or 3D data voxels, it provides an unbiased discrete implementation of such an operator; when used as a model of biological plausible mechanisms, it corresponds to a simple local feedback defined over a small bounded region of any shape inside the parametric space. As such it may be linked to what is processed in a cortical column of the brain and provides an interesting model of general operators corresponding to such a neuronal structure. The present development is illustrated by some experiments of visual motion estimation

An improved biologically plausible trajectory generator

Considering the biological or artificial control of a trajectory generation, we propose a biologically plausible model based on harmonic potentials. Such methods assume that obstacles to avoid (or constraints not to violate) correspond to maxima of the potential, while the goal corresponds to a unique minimum. The corresponding algorithm thus behaves as if one throws a sheet onto this state space, this hyper-surface relief being elevated on obstacles, with a hole at the goal location, so that finding a trajectory reduces to «roll down» along this relief towards the minimal height location. The originality of the present work is to build an harmonic potential (thus without local minimum) as a finite linear combination of elementary harmonic functions. The set of these components samples the border of the admissible domain bounded by obstacles or constraints. This leads to an internal representation of the problem as a non-topographical map increment- ally builded during the system exploration and non-linearly linked to the real problem geometry. As such, it provides a biologically plausible quantitative model of some hippocampus mechanisms and of the related cognitive maps, in coherence with usual biological assumptions about such behavior

An unbiased implementation of regularization mechanisms

In computer or biological vision, computation of vectorial maps of parametric quantities (e.g.: feature parameters, 3D or motion cues, ..) are of common use in perceptual processes. Defining them using continuous partial differential equations yields highly parallelizable regularization processes allowing to obtain well-defined estimations of these quantities. However these equations have to be sampled on real data and this step is not obvious and may introduce some bias. In order to overcome this caveat, a method, introduced by Raviat and developed by Degond and Mas-Gallic, is based on an integral approximation of the diffusion operator used in regularization mechanisms: it leads to a so-called "particle" implementation of such diffusion process. Following this formulation, the present development defines an optimal implementation of such an integral operator with the interesting property that when used on sampled data such as image pixels or 3D data voxels, it provides an unbiased implementation of the corresponding continuous operator without any other approximation. Furthermore, the method is "automatic" (using symbolic computations) in the sense that given a continuous regularization mechanism, the corresponding (non-linear) discrete filter is derived automatically, as made explicit here. A step ahead, the architecture of the implementation corresponds to what is observed in cortical visual maps, leading to a certain biological plausibility . The present development is illustrated by an experiment of visual motion estimation and another experiment in image denoising

Towards biologically plausible regularization mechanisms

This study aims at proposing an implementation of regularization mechanisms compatible with biological operators. More precisely, cortical maps code vectorial parametric quantities, computed by network of neurons. One of these methods is based on an integral approximation of the diffusion operator used in regularization mechanisms. Following this formulation, the present development defines an optimal implementation of such an integral operator with the interesting property that, when used as a model of biological plausible mechanisms, it corresponds to a simple local feedback defined over a small bounded region of the parametric space. This formalism also allows to develop the case of several cortical maps in interaction. We propose simple biologically inspired conditions to guaranty the stability of such interactions. As such it may be linked to what is processed in a cortical column of the brain and provides a biological plausible model of cortical maps computation: here feedbacks between related cortical maps are discussed

To which extend is the "neural code" a metric ?

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 trainsComment: 5 pages 5 figures Proceeding of the conference NeuroComp200

Revisiting time discretisation of spiking network models

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Using an Hebbian learning rule for multi-class SVM classifiers.

http://journals.kluweronline.com/article.asp?PIPS=5384399Regarding biological visual classification, recent series of experiments have enlighten the fact that data classification can be realized in the human visual cortex with latencies of about 100-150 ms, which, considering the visual pathways latencies, is only compatible with a very specific processing architecture, described by models from Thorpe et al. Surprisingly enough, this experimental evidence is in coherence with algorithms derived from the statistical learning theory. More precisely, there is a double link: on one hand, the so-called Vapnik theory offers tools to evaluate and analyze the biological model performances and on the other hand, this model is an interesting front-end for algorithms derived from the Vapnik theory. The present contribution develops this idea, introducing a model derived from the statistical learning theory and using the biological model of Thorpe et al. We experiment its performances using a restrained sign language recognition experiment. This paper intends to be read by biologist as well as statistician, as a consequence basic material in both fields have been reviewed

Simulation neuronale de la vision précoce corticale avec un modèle de Heeger

Une simulation neuronale des cartes corticales des aires V1 impliquées dans les mécanismes de vision précoce (tel que la détection de contour) est reportée ici. Le modèle biologiquement plausible sous-jacent est un modèle de Heeger \cite{boyton-engel-etal:96,simoncelli-heeger:98}. Il a été récemment proposé pour rendre compte de manière plus générale du fonctionnement de ces opérateurs spatio-temporels, que ce que les travaux historiques de Hubel et Wiesel proposaient \cite{hubel-wiesel:- 77,hubel:94}. Notre développement logiciel est basé sur un logiciel libre qui propose une boite à outil pour la simulation de réseaux de neurones permettant de concevoir à la fois des architectures et des modèles neuronaux variés. Notre ajout à été d'impléme- nter les neurones "à-la" Heeger et d'expérimenter une architecture représentan- t les voies visuelles pré-corticales et l'aire corticale V1, sous la restricti- on d'une vision monoculaire et monochromatique. L'interface logiciel réalisée permet aussi de générer des stimulus correspondant à ce qui est usuellement utilisé en neurophysiologie pour de futures comparaison- s entre cette simulation et des données expérimentales effectives