Alessandro Sarti (directeur de recherche au CNRS)

Présentation et informations pratiques pour le séminaire 2015/2016 : voir ici

Organisateurs : Giovanna Citti (University of Bologna), Alain Destexhe (UNIC - CNRS), Olivier Faugeras (INRIA), Yves Fregnac (UNIC - CNRS), Jean-Pierre Nadal (CAMS - EHESS/CNRS), Jean Petitot (CAMS - EHESS), Gabriel Peyre (CEREMADE - CNRS), Alessandro Sarti (CAMS - EHESS/CNRS

Le séminaire sera coorganisé avec, et hébergé par, l'Institut européen de neurosciences théoriques (EITN), 74 Rue du Faubourg Saint-Antoine, 75012 Paris

Séances à venir

Mardi 3 mai 2016, 14h30-16h30, salle de conférence de l'European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris

Florent Meyniel
(CEA, Neurospin Center, France)
A normative account of the sense of confidence during probabilistic learning
The sense of confidence has been studied by psychologists over the past century. It has been under scrutiny only recently in the field of neuroscience. I will briefly review the topic and present the idea that the viewpoints of psychology and neuroscience on confidence can be unified by a definition of confidence as Bayesian probability. After this general introduction, I will present a focused investigation of the sense of confidence in a learning context. Learning in an environment that is both stochastic and changing consists of estimating a model from a limited amount of noisy data. Learning is therefore inherently uncertain, and at least in humans, the learning process is accompanied by a “feeling of knowing” or confidence in what has been learned. The talk will address the characteristics, the origin and the functional role of subjective confidence during learning using behavioral and functional MRI data in humans.
To this end, we developed a probabilistic learning task in which human subjects estimated the transition probabilities between two stimuli in a sequence of observations. The true probabilities changed unexpectedly over time and from time to time, subjects reported their probability estimates as well as their confidence in those estimates. We computed the optimal solution for this learning problem and we used it to analyze subjects' data from a normative viewpoint. Behavioral data showed that humans not only infer a model of their environment, but they also accurately track the likelihood that their inferences are correct. Several characteristics of these confidence reports support that learning and estimating confidence in what has been learned may arise from the same, close-to-optimal probabilistic inference. Functional MRI data showed that the brain may resort to a hierarchical inference to solve this learning problem, and that confidence may be used in the learning algorithm to weight optimally the previously acquired knowledge against and the new incoming evidence.

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Séances passées

Mardi 5 avril 2016, 14h30-16h30, salle de conférence de l'European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris

Bertrand Thirion
(INRIA Saclay-Ile-de-France)
Seeing it all: Convolutional network layers map the function of the human visual system
How to demonstrate and analyze the complexity of visual experiences in a brain mapping framework? The key to this seems to reside in using natural stimulation while increasing the capacity of the analysis system.  In this presentation we discuss a predictive model of brain activity following visual stimulation using the layers of a contest-winning object recognition convolutional network. We find that it explains both high-level and low-level visual areas well and that it can serve as a reliable predictor of brain activity for previously unseen stimuli. We use it to synthesize classical contrast-driven fMRI experiments and analyze the synthetic activity in a conventional way, revealing that the synthesis model captures the known details of the visual system. It is possible to recover classical contrast maps from this model on unseen images.  To expose the brain mapping implicit in the model, we assess how well each contributing layer of the convolutional net fits each voxel. Visualizing these predictive scores reveals a profound  correspondence between convolutional net layer depth and known  hierarchy of visual cortical regions.

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Mardi 1er mars 2016, 14h30-16h30, salle de conférence de l'European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris

Laurent Perrinet
(Institut de Neuroscience de la Timone)
Towards understanding the inferential processes underlying the representation of trajectories in the primary visual cortex
Neural computations in the early visual system are optimized by evolution to efficiently process the trajectory of visual objects in natural scenes and in particular to modulate local mechanisms by the surrounding visual context. In the primary visual cortex, these computations are often characterized by the so-called association field, that is, by the set of rules that combine neighboring visual contour elements to refine more global visual processes. I will first show a simple method to compute the statistics of neighboring contour elements in static images. Surprisingly, we will show that this statistics are sufficient to characterize the category an image belongs to (for instance if it contains an animal), a function usually attributed to higher visual areas. Extending this endeavor to the temporal trajectory of a moving oriented bar, I will present results of a maximum likelihood decoding strategy applied to extracellular activity recorded in the primary visual cortex of behaving macaque monkeys (V1). The orientation and direction decoded in neural activity exhibits the signature of an anticipatory inferential processes optimizing the representation of the bar's trajectory in V1. I will discuss these results in light of a probabilistic model of V1 integrating an explicit knowledge of sensory delays and minimizing its free-energy. This will allow to discuss the implications of these neuronal solutions to the representation of time in the brain, which is essential for the proper fusion of information in the central nervous system.

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Mardi 2 février 2016, 14h30-16h30, salle de conférence de l'European Institute of Theoretical Neuroscience, 74, rue du Faubourg Saint-Antoine 75012, Paris

Jonathan Touboul
(Collège de France & INRIA)
The pinwheel-dipole structure of orientation and spatial frequency, and their common organizing principles
In the early visual cortex of higher mammals, information is processed within functional maps whose layout is thought to underlie visual perception. Here, I will present a few theoretical thoughts together with experimental data on the possible principles at the basis of their architecture, as well as their role in perception. Using new optical imaging data with high resolution, I will show that spatial frequency preference representation exhibits singularities, precisely co-located with pinwheels, and around which the spatial frequency map organizes as an electric dipole potential. This is particularly interesting theoretically: I will demonstrate that both pinwheel and dipoles are the unique topologies ensuring exhaustive representation of both attributes while being optimally parsimonious. Eventually, I will raise the question of the functional advantages and drawbacks of the topology. I will show that the pinwheel dipole topology leaves room for a balanced detection of both attributions. But simulations predict that selectivity shall be sharper near singularity to ensure balanced detection, which I will confirm on biological data. This is a joint work with J. Ribot, A. Romagnoni, C. Milleret and D. Bennequin.

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Mardi 1er décembre 2015, 14h30-16h30, salle de conférence de l'European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris

Sophie Deneve
(Laboratoire de Neurosciences Cognitives, ENS)
Efficiency turns the table on neural encoding, decoding and noise
Sensory neurons are usually described with an encoding model, e.g. a function that predicts their response from the sensory stimulus, e.g. with receptive field (RF) or a tuning curve. However, central to theories of sensory processing is the notion of "efficient coding". We argue here that efficient coding implies a completely different neural coding strategy. Instead of a fixed encoding model, neural populations would be described by a fixed decoding model (i.e. a model reconstructing the stimulus from the neural responses). Because the population solves a global optimization problem, individual neurons are variable, but not noisy, and have no truly invariant tuning curve or receptive field. We review recent experimental evidence and implications for neural noise correlations, robustness and adaptation.

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Mardi 3 novembre 2015, 15h00-16h30, salle de conférence de l'European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris

Daniel Bennequin
(Institut Mathématique de Jussieu & Université Paris 7)
Cohomology for adaptation
Adaptation is a fundamental property of life. We will give examples of rapid adaptation in the sensory system of mammals (visual, vestibular, auditory, ...). Then we will show how in these examples a kind of ternary structure appears, involving transfers, parameters and modular strategies. The notion of co-homology in mathematics will be presented, with examples related to geometry, probability and sensory systems. Then we will show how this  notion should enlight the functioning of ternary structures for adaptation.The particular case of color space, color adaptation and color constancy will be discussed in this context.

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Mardi 16 juin 2015, 14h30-16h30, salle de conférence de l'European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris

Gabriel Peyré
(CNRS & CEREMADE, Université Paris-Dauphine)
Dynamical texture synthesis to probe visual perception
In this talk, I will review statistical models of dynamical textures, targeting applications to computer graphics synthesis and stimulations to probe the visual cortex. I will focus in particular my attention to Gaussian texture models. Despite their simplicity, they are surprisingly effective at capturing micro-textural patterns and simple dynamics. These models can be parameterized as linear stochastic partial differential equations, which makes them easy to learn from exemplar videos and fast to synthesize on the fly. This also opens the door to both  Fourier analysis (power-spectrum parameterization) and an interpretation as an infinite superposition of translated/rotated/scaled elementary "textons". Both interpretations are crucial to allow formalizing psychophysical studies in term of an optimal Bayesian observer. I will show how this explains some psychophysical findings about the influence of texture statistics to bias human speed discrimination (joint work with J. Vacher, L. Perrinet and A. Meso).

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Mardi 5 mai 2015, 14h30-16h30, salle de conférence de l'European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris

Alexandre Afgoustidis
(Institut Mathématique de Jussieu & Université Paris 7)
Orientation maps in the primary visual cortex, gaussian random fields and group representations.
I will first describe some experimental facts on the geometry of orientation maps in the primary visual cortex (area V1) of mammals; this will include the intriguing measurement of a pinwheel (topological singularity) density close to π in very distinct species. The aim of my talk is to identify a few principles that seem necessary for reconstructing this geometry in abstract fashion, and - as a test for their relevance - to use them to introduce V1-like geometries on non-Eucldean spaces. I will focus on theoretical maps which are sampled from Gaussian Random Fields : here the geometrical principles have a simple probabilistic expression, and a natural interpretation in terms of the unitary representations of the Euclidean group of rigid plane motions. Using representations of other groups to shift to non Euclidean geometries might help us understand the conceptual significance of the experimental observations on pinwheel densities.

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Mardi 31 mars 2015, 14h30-16h30, salle de conférence de l'European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris

Khashayar Pakdaman
(Institut Jacques Monod, Groupe biologie computationnelle et biomathématiques )
On some aspects of synchronization and spontaneous activity in neuronal
Spontaneous activity is ubiquitous in neuronal assemblies and takes on a variety of forms. Motivated by experimental studies on such activity in brain stem slices, this presentation will review modelling aspects and their theoretical analysis with specific emphasis on the emergence of synchrony.

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Mardi 3 février 2015, 14h30-16h30, salle de conférence de l'European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris

Gregory Faye
Traveling pulses in neural field equations
In this seminar, I will present some recent work on traveling pulses in neural field equations. More precisely, we explore how local negative feedbacks (linear adaptation or synaptic depression) impact the generation of traveling pulses. We will use techniques ranging from singular perturbation theory, Fredholm operators and Evans functions to study the existence and stability of such traveling waves.

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Mardi 2 décembre 2014, 14h30-16h30, salle de conférence de l'European Institute of Theoretical Neuroscience, rue du Faubourg Saint-Antoine 75012, Paris

Davide Barbieri
(Mathematics Department, Universidad Autonoma de Madrid)
Simple cells receptive fields and orientation preference maps : A Lie group approach for the analysis of fundamental morphologies of V1
Work in collaboration with G. Citti, G. Sanguinetti and A. Sarti
Simple cells classical receptive fields can be accurately modeled by Gaussian Gabor functions. However, this a-priori 6 parameters family (including positions, frequencies and scales) is represented on an essentially two dimensional cortical layer. This implies that only a subset of the parameter space is actually available to the linear filtering of visual stimuli performed by V1.
We will first discuss a fundamental property of the family of implemented parameters, namely the distribution of the shape index, which measures the number of on and off regions of receptive fields by relating frequencies to scales. We will show that it can be effectively quantified in terms of the uncertainty principle associated to the complementary symmetries of the parameter space, that are given by the group of translations and rotations of the Euclidean plane SE(2). The main argument is the effort to keep the highest possible resolution in the detection of position and orientation allowed by the dimensional constraint.
Then we will enter a more detailed study of the SE(2) group, and show that its irreducible representations can be used to provide an accurate model for orientation preference maps. In particular, we will see that the associated continuous wavelet transform allows to effectively reproduce the maps of activation of V1 in response to gratings, whenever the mother wavelet is a fundamental minumum of the uncertainty principle and the analyzed signal is white noise. In this case we can also prove that the wavelet transform is injective, which implies uniqueness of the white noise source, despite not being square integrable. Moreover, its complex regularity inherited by the uncertainty principle allows to obtain it as the two dimensional Bargmann transform of a purely directional signal, hence characterizing all possible configurations of such activated regions.

Présentation générale du séminaire

Les récents développements des neurosciences de la perception permettent de commencer à modéliser mathématiquement les mécanismes neuronaux de la perception et, en particulier, de la vision. Cela ouvre de nouvelles perspectives sur la genèse de la perception visuelle. Un aspect essentiel de cette problématique concerne les liens mathématiques entre l'analyse du signal sensoriel et la structuration géométrique des représentations perceptives. La Neuromathématique de la vision développe, en relation étroite avec un vaste ensemble de données expérimentales, plusieurs modèles mathématiques du cortex visuel et propose de modèles géométriques de son architecture fonctionnelle, c'est-à-dire de l'organisation de ses connexions neurales. Son propos est d'expliciter la neuromathématique immanente à la perception visuelle et en définitive d'éclairer la codification neuronale des représentations spatiales. Dans la mesure où l'origine des représentations spatiales constitue un problème majeur non seulement scientifique mais aussi philosophique, la recherche d'architectures fonctionnelles possède une forte dimension épistémologique.

La recherche des architectures fonctionnelles immanente à la vision concerne en définitive la codification neuronale des représentations spatiales. On ne parle pas ici d’une origine neuronale des représentations, car les organisations neuronales sont générées à leur tour parmi des processus d'apprentissage dans l'interaction entre le sujet et le monde. Donc, il devient crucial de clarifier les relations entre les structures de la neurogéometrie (différentielles, métrique, de groupe) et les pratiques vécues des sujets vivants. Le problème de l'origine de l'espace est renvoyé dans la boucle des processus concurrents d'objectivation et de subjectivation.

Dans ce cadre, le problème fondamental de la constitution des unités perceptives sera considéré par rapport aux équations de populations neurales définies sur la structure de connectivité corticale. Ces équations expriment, au travers de leurs équivariances, les rapports profonds qui les relient à la géométrie. L’évolution dynamique des populations, et notamment les bifurcations des solutions des équations qui les régissent, agit comme une opération d'individuation des structures saillantes, qui correspondent notamment aux unités gestaltiques. Ces phénomènes émergents peuvent aussi apparaître dans des modélisations qui relient les descriptions microscopiques des phénomènes (le niveau des neurones individuels) au niveau macroscopique (les populations de neurones des aires corticales de la vision). Ces approches, dites de champ moyen, ont prouvé leur efficacité en physique et sont très prometteuses en neurosciences où elles fournissent à la fois des descriptions parcimonieuses de vastes ensembles neuronaux tout en rendant compte de phénomènes émergents. Il est important de souligner que le caractère global/holistique du processus d'émergence perceptive est respecté dans cette approche, qui échappe chaque critique de réductionnisme.

Nous proposons la constitution d'un séminaire organisé par un petit groupe de scientifiques qui unissent leurs efforts pour explorer cette approche mathématisant la cognition visuelle. Ils organiseront un séminaire régulier et diffuseront les thèmes de leurs réflexions au moyen de cycles de conférences. Ils tenteront aussi de répondre à la demande de communication avec les mathématiciens que peuvent avoir des chercheurs en sciences cognitives, plus particulièrement ceux qui travaillent sur la perception visuelle dans ses rapports avec la géométrie.

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