432 research outputs found
From Twentieth Annual Computational Neuroscience Meeting: CNS*2011 Stockholm, Sweden. 23-28 July 2011
No full textPublished by BioMed Central
Schultze-Kraft, Matthias ; Diesmann, Markus ; Grün, Sonja ; Helias, Moritz : Correlation transmission of spiking neurons is boosted by synchronous input : From Twentieth Annual Computational Neuroscience Meeting: CNS*2011 Stockholm, Sweden. 23-28 July 2011. - In: BMC Neuroscience. - ISSN 1471-2202 (online). - 12 (2011), suppl. 1, P144. - doi:10.1186/1471-2202-12-S1-P144
Correlations, chaos, and criticality in neural networks
No full textCorrelations, chaos, and criticality in neural networksMoritz HeliasINM-6 Juelich Research CentreTheory of condensed matter physicsRWTH AachenThe remarkable properties of information-processing of biological andof artificial neuronal networks alike arise from the interaction oflarge numbers of neurons. A central quest is thus to characterizetheir collective states. The directed coupling between pairs ofneurons and their continuous dissipation of energy, moreover, causedynamics of neuronal networks outside thermodynamic equilibrium.Tools from non-equilibrium statistical mechanics and field theory arethus instrumental to obtain a quantitative understanding. We herepresent progress with this recent approach [1].On the experimental side, we show how correlations betweenpairs of neurons are informative on the dynamics ofcortical networks: they are poised near a transition to chaos [2].Close to this transition, we find prolongued sequential memoryfor past signals [3]. In the chaotic regime, networks offerrepresentations of information whose dimensionality expands with time.We show how this mechanism aids classification performance [3].Together these works illustrate the fruitful interplay betweentheoretical physics, neuronal networks, and neural informationprocessing.1. Helias, Dahmen (2020) Statistical field theory for neural networks.Springer lecture notes in physics.2. Dahmen D, Grün S, Diesmann M, Helias M (2019). Second type of criticality in the brain uncovers rich multiple-neuron dynamics. PNAS 116 (26) 13051-130603. Schuecker J, Goedeke S, Helias M (2018). Optimal sequence memory in driven random networks. Phys Rev X 8, 0410294. Keup, Kuehn, Dahmen, Helias (2020) Transient chaotic dimensionality expansion by recurrent networks. arXiv:2002.11006 [cond-mat.dis-nn
Wave trains
No full textCode used to create all figures of the manuscript: Johanna Senk, Karolína Korvasová, Jannis Schuecker, Espen Hagen, Tom Tetzlaff, Markus Diesmann and Moritz Helias "Conditions for wave trains in spiking neural networks". Accepted for publication in Physical Review Researc
Dynamical and statistical structure of spatially organized neuronal networks
No full textThe cerebral cortex, the outer layer of mammalian brains, comprises a vast number of neurons arranged and connected in a highly organized fashion. The likelihood of neurons to be connected and how fast they may exchange signals depends, among other properties, on their spatial distance. Cortical networks may be well described as completely random networks on microscopic scales because cortical neurons have essentially uniform connection probabilities within a few tens of micrometers. However, the distance-dependence of neuronal connections certainly is important on mesoscopic scales spanning several millimeters, where many neurons are most likely unconnected. While the theory of random networks is already well-established, how such a spatial organization affects a network's activity is not yet fully understood. The objective of this thesis is to provide an overview of the current analytical understanding of spatially organized networks on a mesoscopic scale, as well as to advance this understanding with three studies covering complementary aspects of spatially organized network theory.A variety of experimental recordings in cortex reveals that neuronal activity is coordinated across several millimeters: Multi-electrode-arrays covering a few square millimeters, for example, provide access to the local field potential, a measure of population activity, as well as single neuron spiking activity. While spiking activity exhibits distance-dependent correlation characteristics, population activity shows spatio-temporally coherent activity, like periodic patterns, waves, or bumps. In this thesis we employ a combination of network models, analytical tools, and simulations to gain an understanding of such findings. We particularly make use of mean-field theory, which is a viable tool for investigating statistical properties of populations made up of thousands of neurons, and it therefore may be utilized to gain a coarse-grained description of network activity at large scales. In the first main part, we present a Python package we developed to make previously developed analytical results from neuronal network mean-field theory applicable to concrete network models, giving access to estimates of model properties such as firing rates and power spectra, as well as more elaborate tools that can support network modeling. In the second study, we investigate how neurons may coordinate their activity dynamically across large distances, without the need for highly correlated input or long-range connections. In the third study, we explore how a temporal delay may affect pattern formation in planar networks. As we demonstrate, spatial organization is a critical network feature that does not merely lead to obvious phenomena like spatially structured activity. On the contrary, as we show in this thesis, spatial organization leads to a variety of interesting, non-trivial effects, that on first sight might even seem counterintuitive, and this topic certainly provides a multitude of intriguing research questions for the near future
Neuronal architecture extracts statistical temporal patterns
No full text<p>This repository contains the code used to create all figures of the manuscript:</p>
<p>Nestler, S., Helias, M., & Gilson, M. (2023). Neuronal architecture extracts statistical temporal patterns. arXiv preprint arXiv:2301.10203.</p>
Transient chaotic dimensionality expansion by recurrent networks
No full textTransient chaotic dimensionality expansion by recurrent networksMoritz HeliasINM-6, Juelich Research CentreFaculty of Physics, RWTH Aachen UniversityCortical neurons communicate with spikes, which are discrete events intime and value. They often show optimal computational performance close toa transition to rate-chaos; chaos that is driven by local and smooth averagesof the discrete activity.We here analyze microscopic and rate chaos in discretely-coupled networksof binary neurons by a model-independent field theory. We find a stronglynetwork size-dependent transition to microscopic chaos and a chaoticsubmanifold that spans only a finite fraction of the entire activity space.Rate chaos is shown to be impossible in these networks.Applying stimuli to a strongly microscopically chaotic binary networkthat acts as a reservoir, one observes a transient expansion of thedimensionality of the representing neuronal space. Crucially, the numberof dimensions corrupted by noise lags behind the informative dimensions.This translates to a transient peak in the networks' classification performanceeven deeply in the chaotic regime, extending the view that computationalperformance is always optimal near the edge of chaos. Classificationperformance peaks rapidly within one activation per neuron, demonstratingfast event-based computation. The generality of this mechanism isunderlined by simulations of spiking networks of leaky integrate-and fireneurons.1. Keup, Kuehn, Dahmen, Helias (2020) Transient chaotic dimensionality expansion by recurrent networks. arXiv:2002.11006 [cond-mat.dis-nn
Code and data for:Keup et al. (2021) Transient Chaotic Dimensionality Expansion by Recurrent Networks. PRX 11, 021064
No full textSimulation data, python code and figures used in the publicationKeup, Kühn, Dahmen, Helias (2021) Transient chaotic dimensionality expansion by recurrent networks. Physical Review X 11, 021064, doi: 10.1103/PhysRevX.11.021064.Please see README.md for a detailed description and execution instructions
CNS*2015 Tutorial - theory of correlations in recurrent networks
No full textIn the first part of this tutorial, we introduce the mathematical tools to determine firing statistics of neurons receiving fluctuating input form a network. We show how one can apply an efficient Fokker-Planck method to derive the neurons’ output statistics whenever the input can be assumed to be Gaussian white (iid) noise. We further study more realistic cases, where the input fluctuations depart from the iid assumptions. Using the integrate-and-fire neuron model, we will demonstrate how to compute the firing rate, auto-correlation and cross-correlation functions of the output spike trains. The transfer function of the output correlations given the time scale of the input correlations will be discussed [Moreno-Bote and Parga, 2006, Brunel et al 2001]. In particular, we will show that the output correlations are generally weaker than the input correlations and how the working regime of the neuron shapes the cross-correlation functions [Ostojic et al., 2009; Helias et al., 2013]. We conclude the first part by investigating the relation between neurons’ pairwise correlation due commen fluctuations and their firing rates [de la Rocha et al., 2007].In the second part, we will consider correlations in recurrent random networks. Using a binary neuron model [Ginzburg & Sompolinsky, 1994], we explain how mean-field theory determines the stationary state and how the network-generated noise linearizes the single neuron response. The resulting linear equation for the fluctuations in recurrent networks is then solved to obtain the correlation structure in balanced random networks. We discuss two different points of view of the recently reported active suppression of correlations in balanced networks by fast tracking [Renart et al., 2010] and by negative feedback [Tetzlaff et al., 2012]. Finally, we consider extensions of the theory of correlations of linear Poisson spiking models [Hawkes, 1971, Pernice et al. 2011] to the leaky integrate-and-fire model [Trousdale et al. 2012, Pernice et al. 2012] and present a unifying view of linear response theory of weak correlations [Grytskyy et al, 2013]
Expanding the effective action around non-Gaussian theories
No full textThe effective action or Gibbs Free Energy is the central quantity to study phase transitions and is at the core of effective theories constructed, for example, by the renormalization group. It is known that only one-line-irreducible Feynman diagrams contribute in the case that the theory, about which one expands, is Gaussian. We introduce a generalized notion of one-line-irreducibility: diagrams that remain connected after detaching a single leg of an interaction vertex. We show that the effective action decomposes into diagrams that are either irreducible in this more general sense or belong to a second class of diagrams that has no analogue in Gaussian theories [Kühn & Helias 2017, arXiv:1711.05599]. The presented method allows the efficient diagrammatic perturbative computation of the effective action around any exactly solvable problem. We illustrate this method by application to the (classical) Ising model expanded in the coupling strength. This reproduces the Plefka expansion [Plefka 1982], including the TAP-correction [Thouless et al. 1977] to mean-field theory. We find that the diagrammatic formulation considerably simplifies the calculation compared to existing techniques [Takayama & Nakanishi 1997, Georges & Yedidia 1991]. Supported by the Helmholtz foundation (VH-NG-1028, SMHB); EU Grant 604102 (HBP)
Expansion of the effective action around non-Gaussian theories
No full textThe effective action or Gibbs Free Energy is the central quantity to study phase transitions and is at the core of effective theories constructed, for example, by the renormalization group. It is known that only one-line-irreducible Feynman diagrams contribute in the case that the theory, about which one expands, is Gaussian. We introduce a generalized notion of one-line-irreducibility: diagrams that remain connected after detaching a single leg of an interaction vertex. We show that the effective action decomposes into diagrams that are either irreducible in this more general sense or belong to a second class of diagrams that has no analogue in Gaussian theories [Kuehn & Helias 2017, arXiv:1711.05599]. The presented method allows the efficient diagrammatic perturbative computation of the effective action around any exactly solvable problem.We illustrate this method by application to the (classical) Ising model expanded in the coupling strength. This reproduces the Plefka expansion [Plefka 1982], including the TAP-correction [Thouless et al. 1977] to mean-field theory. We find that the diagrammatic formulation considerably simplifies the calculation compared to existing techniques [Takayama & Nakanishi 1997, Georges & Yedidia 1991].Supported by the Helmholtz foundation (VH-NG-1028, SMHB); EU Grant 604102 (HBP)
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