arXiv subjects

Olivier Marre

Publications and source records attributed to Olivier Marre.

28 records · Page 2Linked to original sources

arXiv2016

Nonlinear decoding of a complex movie from the mammalian retina

Retinal circuitry transforms spatiotemporal patterns of light into spiking activity of ganglion cells, which provide the sole visual input to the brain. Recent advances have led to a detailed characterization of retinal activity and stimulus encoding by large neural populations. The inverse problem of decoding, where the stimulus is reconstructed from spikes, has received less attention, in particular for complex input movies that should be reconstructed "pixel-by-pixel". We recorded around a hundred neurons from a dense patch in a rat retina and decoded movies of multiple small discs executing mutually-avoiding random motions. We constructed nonlinear (kernelized) decoders that improved significantly over linear decoding results, mostly due to their ability to reliably separate between neural responses driven by locally fluctuating light signals, and responses at locally constant light driven by spontaneous or network activity. This improvement crucially depended on the precise, non-Poisson temporal structure of individual spike trains, which originated in the spike-history dependence of neural responses. Our results suggest a general paradigm in which downstream neural circuitry could discriminate between spontaneous and stimulus-driven activity on the basis of higher-order statistical structure intrinsic to the incoming spike trains.

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arXiv2015

Dynamical criticality in the collective activity of a population of retinal neurons

Recent experimental results based on multi-electrode and imaging techniques have reinvigorated the idea that large neural networks operate near a critical point, between order and disorder. However, evidence for criticality has relied on the definition of arbitrary order parameters, or on models that do not address the dynamical nature of network activity. Here we introduce a novel approach to assess criticality that overcomes these limitations, while encompassing and generalizing previous criteria. We find a simple model to describe the global activity of large populations of ganglion cells in the rat retina, and show that their statistics are poised near a critical point. Taking into account the temporal dynamics of the activity greatly enhances the evidence for criticality, revealing it where previous methods would not. The approach is general and could be used in other biological networks.

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arXiv2014

High accuracy decoding of dynamical motion from a large retinal population

Motion tracking is a challenge the visual system has to solve by reading out the retinal population. Here we recorded a large population of ganglion cells in a dense patch of salamander and guinea pig retinas while displaying a bar moving diffusively. We show that the bar position can be reconstructed from retinal activity with a precision in the hyperacuity regime using a linear decoder acting on 100+ cells. The classical view would have suggested that the firing rates of the cells form a moving hill of activity tracking the bar's position. Instead, we found that ganglion cells fired sparsely over an area much larger than predicted by their receptive fields, so that the neural image did not track the bar. This highly redundant organization allows for diverse collections of ganglion cells to represent high-accuracy motion information in a form easily read out by downstream neural circuits.

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arXiv2014

Thermodynamics for a network of neurons: Signatures of criticality

The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but with more spikes the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N=160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. Networks with more or less correlation among neurons would not reach this critical state. We suggest further tests of criticality, and give a brief discussion of its functional significance.

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arXiv2013

Predictive information in a sensory population

Guiding behavior requires the brain to make predictions about future sensory inputs. Here we show that efficient predictive computation starts at the earliest stages of the visual system. We estimate how much information groups of retinal ganglion cells carry about the future state of their visual inputs, and show that every cell we can observe participates in a group of cells for which this predictive information is close to the physical limit set by the statistical structure of the inputs themselves. Groups of cells in the retina also carry information about the future state of their own activity, and we show that this information can be compressed further and encoded by downstream predictor neurons, which then exhibit interesting feature selectivity. Efficient representation of predictive information is a candidate principle that can be applied at each stage of neural computation.

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arXiv2013

Searching for collective behavior in a network of real neurons

Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such "K-pairwise" models--being systematic extensions of the previously used pairwise Ising models--provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.

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arXiv2012

Spatio-temporal spike trains analysis for large scale networks using maximum entropy principle and Monte-Carlo method

Understanding the dynamics of neural networks is a major challenge in experimental neuroscience. For that purpose, a modelling of the recorded activity that reproduces the main statistics of the data is required. In a first part, we present a review on recent results dealing with spike train statistics analysis using maximum entropy models (MaxEnt). Most of these studies have been focusing on modelling synchronous spike patterns, leaving aside the temporal dynamics of the neural activity. However, the maximum entropy principle can be generalized to the temporal case, leading to Markovian models where memory effects and time correlations in the dynamics are properly taken into account. In a second part, we present a new method based on Monte-Carlo sampling which is suited for the fitting of large-scale spatio-temporal MaxEnt models. The formalism and the tools presented here will be essential to fit MaxEnt spatio-temporal models to large neural ensembles.

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arXiv2012

Learning quadratic receptive fields from neural responses to natural stimuli

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are only selective for a small number of linear projections of a potentially high-dimensional input. Here we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g. naturalistic) stimulus distribution, we review several inference methods, focussing in particular on two information-theory-based approaches (maximization of stimulus energy or of noise entropy) and a likelihood-based approach (Bayesian spike-triggered covariance, extensions of generalized linear models). We analyze the formal connection between the likelihood-based and information-based approaches to show how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.

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arXiv2012

The simplest maximum entropy model for collective behavior in a neural network

Recent work emphasizes that the maximum entropy principle provides a bridge between statistical mechanics models for collective behavior in neural networks and experiments on networks of real neurons. Most of this work has focused on capturing the measured correlations among pairs of neurons. Here we suggest an alternative, constructing models that are consistent with the distribution of global network activity, i.e. the probability that K out of N cells in the network generate action potentials in the same small time bin. The inverse problem that we need to solve in constructing the model is analytically tractable, and provides a natural "thermodynamics" for the network in the limit of large N. We analyze the responses of neurons in a small patch of the retina to naturalistic stimuli, and find that the implied thermodynamics is very close to an unusual critical point, in which the entropy (in proper units) is exactly equal to the energy.

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arXiv2009

Prediction of spatio-temporal patterns of neural activity from pairwise correlations

We designed a model-based analysis to predict the occurrence of population patterns in distributed spiking activity. Using a maximum entropy principle with a Markovian assumption, we obtain a model that accounts for both spatial and temporal pairwise correlations among neurons. This model is tested on data generated with a Glauber spin-glass system and is shown to correctly predict the occurrence probabilities of spatio-temporal patterns significantly better than Ising models taking into account only pairwise correlations. This increase of predictability was also observed on experimental data recorded in parietal cortex during slow-wave sleep. This approach can also be used to generate surrogates that reproduce the spatial and temporal correlations of a given data set.

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