arXiv subjects

Markus Diesmann

Publications and source records attributed to Markus Diesmann.

At least 37 records · Page 2Linked to original sources

arXiv2021

Prominent characteristics of recurrent neuronal networks are robust against low synaptic weight resolution

The representation of the natural-density, heterogeneous connectivity of neuronal network models at relevant spatial scales remains a challenge for Computational Neuroscience and Neuromorphic Computing. In particular, the memory demands imposed by the vast number of synapses in brain-scale network simulations constitutes a major obstacle. Limiting the number resolution of synaptic weights appears to be a natural strategy to reduce memory and compute load. In this study, we investigate the effects of a limited synaptic-weight resolution on the dynamics of recurrent spiking neuronal networks resembling local cortical circuits, and develop strategies for minimizing deviations from the dynamics of networks with high-resolution synaptic weights. We mimic the effect of a limited synaptic weight resolution by replacing normally distributed synaptic weights by weights drawn from a discrete distribution, and compare the resulting statistics characterizing firing rates, spike-train irregularity, and correlation coefficients with the reference solution. We show that a naive discretization of synaptic weights generally leads to a distortion of the spike-train statistics. Only if the weights are discretized such that the mean and the variance of the total synaptic input currents are preserved, the firing statistics remains unaffected for the types of networks considered in this study. For networks with sufficiently heterogeneous in-degrees, the firing statistics can be preserved even if all synaptic weights are replaced by the mean of the weight distribution. We conclude that even for simple networks with non-plastic neurons and synapses, a discretization of synaptic weights can lead to substantial deviations in the firing statistics, unless the discretization is performed with care and guided by a rigorous validation process.

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arXiv2021

Event-based update of synapses in voltage-based learning rules

Due to the point-like nature of neuronal spiking, efficient neural network simulators often employ event-based simulation schemes for synapses. Yet many types of synaptic plasticity rely on the membrane potential of the postsynaptic cell as a third factor in addition to pre- and postsynaptic spike times. Synapses therefore require continuous information to update their strength which a priori necessitates a continuous update in a time-driven manner. The latter hinders scaling of simulations to realistic cortical network sizes and relevant time scales for learning. Here, we derive two efficient algorithms for archiving postsynaptic membrane potentials, both compatible with modern simulation engines based on event-based synapse updates. We theoretically contrast the two algorithms with a time-driven synapse update scheme to analyze advantages in terms of memory and computations. We further present a reference implementation in the spiking neural network simulator NEST for two prototypical voltage-based plasticity rules: the Clopath rule and the Urbanczik-Senn rule. For both rules, the two event-based algorithms significantly outperform the time-driven scheme. Depending on the amount of data to be stored for plasticity, which heavily differs between the rules, a strong performance increase can be achieved by compressing or sampling of information on membrane potentials. Our results on computational efficiency related to archiving of information provide guidelines for the design of learning rules in order to make them practically usable in large-scale networks.

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arXiv2020

Usage and Scaling of an Open-Source Spiking Multi-Area Model of Monkey Cortex

We are entering an age of `big' computational neuroscience, in which neural network models are increasing in size and in numbers of underlying data sets. Consolidating the zoo of models into large-scale models simultaneously consistent with a wide range of data is only possible through the effort of large teams, which can be spread across multiple research institutions. To ensure that computational neuroscientists can build on each other's work, it is important to make models publicly available as well-documented code. This chapter describes such an open-source model, which relates the connectivity structure of all vision-related cortical areas of the macaque monkey with their resting-state dynamics. We give a brief overview of how to use the executable model specification, which employs NEST as simulation engine, and show its runtime scaling. The solutions found serve as an example for organizing the workflow of future models from the raw experimental data to the visualization of the results, expose the challenges, and give guidance for the construction of ICT infrastructure for neuroscience.

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arXiv2020

Bringing Anatomical Information into Neuronal Network Models

For constructing neuronal network models computational neuroscientists have access to wide-ranging anatomical data that nevertheless tend to cover only a fraction of the parameters to be determined. Finding and interpreting the most relevant data, estimating missing values, and combining the data and estimates from various sources into a coherent whole is a daunting task. With this chapter we aim to provide guidance to modelers by describing the main types of anatomical data that may be useful for informing neuronal network models. We further discuss aspects of the underlying experimental techniques relevant to the interpretation of the data, list particularly comprehensive data sets, and describe methods for filling in the gaps in the experimental data. Such methods of `predictive connectomics' estimate connectivity where the data are lacking based on statistical relationships with known quantities. It is instructive, and in certain cases necessary, to use organizational principles that link the plethora of data within a unifying framework where regularities of brain structure can be exploited to inform computational models. In addition, we touch upon the most prominent features of brain organization that are likely to influence predicted neuronal network dynamics, with a focus on the mammalian cerebral cortex. Given the still existing need for modelers to navigate a complex data landscape full of holes and stumbling blocks, it is vital that the field of neuroanatomy is moving toward increasingly systematic data collection, representation, and publication.

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arXiv2019

Conditions for wave trains in spiking neural networks

Spatiotemporal patterns such as traveling waves are frequently observed in recordings of neural activity. The mechanisms underlying the generation of such patterns are largely unknown. Previous studies have investigated the existence and uniqueness of different types of waves or bumps of activity using neural-field models, phenomenological coarse-grained descriptions of neural-network dynamics. But it remains unclear how these insights can be transferred to more biologically realistic networks of spiking neurons, where individual neurons fire irregularly. Here, we employ mean-field theory to reduce a microscopic model of leaky integrate-and-fire (LIF) neurons with distance-dependent connectivity to an effective neural-field model. In contrast to existing phenomenological descriptions, the dynamics in this neural-field model depends on the mean and the variance in the synaptic input, both determining the amplitude and the temporal structure of the resulting effective coupling kernel. For the neural-field model we employ liner stability analysis to derive conditions for the existence of spatial and temporal oscillations and wave trains, that is, temporally and spatially periodic traveling waves. We first prove that wave trains cannot occur in a single homogeneous population of neurons, irrespective of the form of distance dependence of the connection probability. Compatible with the architecture of cortical neural networks, wave trains emerge in two-population networks of excitatory and inhibitory neurons as a combination of delay-induced temporal oscillations and spatial oscillations due to distance-dependent connectivity profiles. Finally, we demonstrate quantitative agreement between predictions of the analytically tractable neural-field model and numerical simulations of both networks of nonlinear rate-based units and networks of LIF neurons.

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arXiv2019

The scientific case for brain simulations

A key element of the European Union's Human Brain Project (HBP) and other large-scale brain research projects is simulation of large-scale model networks of neurons. Here we argue why such simulations will likely be indispensable for bridging the scales between the neuron and system levels in the brain, and a set of brain simulators based on neuron models at different levels of biological detail should thus be developed. To allow for systematic refinement of candidate network models by comparison with experiments, the simulations should be multimodal in the sense that they should not only predict action potentials, but also electric, magnetic, and optical signals measured at the population and system levels.

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arXiv2018

VIOLA - A multi-purpose and web-based visualization tool for neuronal-network simulation output

Neuronal network models and corresponding computer simulations are invaluable tools to aid the interpretation of the relationship between neuron properties, connectivity and measured activity in cortical tissue. Spatiotemporal patterns of activity propagating across the cortical surface as observed experimentally can for example be described by neuronal network models with layered geometry and distance-dependent connectivity. The interpretation of the resulting stream of multi-modal and multi-dimensional simulation data calls for integrating interactive visualization steps into existing simulation-analysis workflows. Here, we present a set of interactive visualization concepts called views for the visual analysis of activity data in topological network models, and a corresponding reference implementation VIOLA (VIsualization Of Layer Activity). The software is a lightweight, open-source, web-based and platform-independent application combining and adapting modern interactive visualization paradigms, such as coordinated multiple views, for massively parallel neurophysiological data. For a use-case demonstration we consider spiking activity data of a two-population, layered point-neuron network model subject to a spatially confined excitation originating from an external population. With the multiple coordinated views, an explorative and qualitative assessment of the spatiotemporal features of neuronal activity can be performed upfront of a detailed quantitative data analysis of specific aspects of the data. Furthermore, ongoing efforts including the European Human Brain Project aim at providing online user portals for integrated model development, simulation, analysis and provenance tracking, wherein interactive visual analysis tools are one component. Browser-compatible, web-technology based solutions are therefore required. Within this scope, with VIOLA we provide a first prototype.

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arXiv2017

Deterministic networks for probabilistic computing

Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own private source of randomness, often in the form of uncorrelated external noise. However, both in vivo and in silico, the number of noise sources is limited due to space and bandwidth constraints. Hence, neurons in large networks usually need to share noise sources. Here, we show that the resulting shared-noise correlations can significantly impair the performance of stochastic network models. We demonstrate that this problem can be overcome by using deterministic recurrent neural networks as sources of uncorrelated noise, exploiting the decorrelating effect of inhibitory feedback. Consequently, even a single recurrent network of a few hundred neurons can serve as a natural noise source for large ensembles of functional networks, each comprising thousands of units. We successfully apply the proposed framework to a diverse set of binary-unit networks with different dimensionalities and entropies, as well as to a network reproducing handwritten digits with distinct predefined frequencies. Finally, we show that the same design transfers to functional networks of spiking neurons.

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arXiv2017

Perfect spike detection via time reversal

Spiking neuronal networks are usually simulated with three main simulation schemes: the classical time-driven and event-driven schemes, and the more recent hybrid scheme. All three schemes evolve the state of a neuron through a series of checkpoints: equally spaced in the first scheme and determined neuron-wise by spike events in the latter two. The time-driven and the hybrid scheme determine whether the membrane potential of a neuron crosses a threshold at the end of of the time interval between consecutive checkpoints. Threshold crossing can, however, occur within the interval even if this test is negative. Spikes can therefore be missed. The present work derives, implements, and benchmarks a method for perfect retrospective spike detection. This method can be applied to neuron models with affine or linear subthreshold dynamics. The idea behind the method is to propagate the threshold with a time-inverted dynamics, testing whether the threshold crosses the neuron state to be evolved, rather than vice versa. Algebraically this translates into a set of inequalities necessary and sufficient for threshold crossing. This test is slower than the imperfect one, but faster than an alternative perfect tests based on bisection or root-finding methods. Comparison confirms earlier results that the imperfect test rarely misses spikes (less than a fraction $1/10^8$ of missed spikes) in biologically relevant settings. This study offers an alternative geometric point of view on neuronal dynamics.

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arXiv2017

LFP beta amplitude is predictive of mesoscopic spatio-temporal phase patterns

Beta oscillations observed in motor cortical local field potentials (LFPs) recorded on separate electrodes of a multi-electrode array have been shown to exhibit non-zero phase shifts that organize into a planar wave propagation. Here, we generalize this concept by introducing additional classes of patterns that fully describe the spatial organization of beta oscillations. During a delayed reach-to-grasp task in monkey primary motor and dorsal premotor cortices we distinguish planar, synchronized, random, circular, and radial phase patterns. We observe that specific patterns correlate with the beta amplitude (envelope). In particular, wave propagation accelerates with growing amplitude, and culminates at maximum amplitude in a synchronized pattern. Furthermore, the occurrence probability of a particular pattern is modulated with behavioral epochs: Planar waves and synchronized patterns are more present during movement preparation where beta amplitudes are large, whereas random phase patterns are dominant during movement execution where beta amplitudes are small.

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arXiv2017

Fundamental activity constraints lead to specific interpretations of the connectome

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to experimental observations. Nevertheless, structurally realistic network models of spiking neurons are necessarily underconstrained even if experimental data on brain connectivity are incorporated to the best of our knowledge. Guided by physiological observations, any model must therefore explore the parameter ranges within the uncertainty of the data. Based on simulation results alone, however, the mechanisms underlying stable and physiologically realistic activity often remain obscure. We here employ a mean-field reduction of the dynamics, which allows us to include activity constraints into the process of model construction. We shape the phase space of a multi-scale network model of the vision-related areas of macaque cortex by systematically refining its connectivity. Fundamental constraints on the activity, i.e., prohibiting quiescence and requiring global stability, prove sufficient to obtain realistic layer- and area-specific activity. Only small adaptations of the structure are required, showing that the network operates close to an instability. The procedure identifies components of the network critical to its collective dynamics and creates hypotheses for structural data and future experiments. The method can be applied to networks involving any neuron model with a known gain function.

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arXiv2016

Integration of continuous-time dynamics in a spiking neural network simulator

Contemporary modeling approaches to the dynamics of neural networks consider two main classes of models: biologically grounded spiking neurons and functionally inspired rate-based units. The unified simulation framework presented here supports the combination of the two for multi-scale modeling approaches, the quantitative validation of mean-field approaches by spiking network simulations, and an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes. While most efficient spiking simulations rely on the communication of discrete events, rate models require time-continuous interactions between neurons. Exploiting the conceptual similarity to the inclusion of gap junctions in spiking network simulations, we arrive at a reference implementation of instantaneous and delayed interactions between rate-based models in a spiking network simulator. The separation of rate dynamics from the general connection and communication infrastructure ensures flexibility of the framework. We further demonstrate the broad applicability of the framework by considering various examples from the literature ranging from random networks to neural field models. The study provides the prerequisite for interactions between rate-based and spiking models in a joint simulation.

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arXiv2016

The effect of heterogeneity on decorrelation mechanisms in spiking neural networks: a neuromorphic-hardware study

High-level brain function such as memory, classification or reasoning can be realized by means of recurrent networks of simplified model neurons. Analog neuromorphic hardware constitutes a fast and energy efficient substrate for the implementation of such neural computing architectures in technical applications and neuroscientific research. The functional performance of neural networks is often critically dependent on the level of correlations in the neural activity. In finite networks, correlations are typically inevitable due to shared presynaptic input. Recent theoretical studies have shown that inhibitory feedback, abundant in biological neural networks, can actively suppress these shared-input correlations and thereby enable neurons to fire nearly independently. For networks of spiking neurons, the decorrelating effect of inhibitory feedback has so far been explicitly demonstrated only for homogeneous networks of neurons with linear sub-threshold dynamics. Theory, however, suggests that the effect is a general phenomenon, present in any system with sufficient inhibitory feedback, irrespective of the details of the network structure or the neuronal and synaptic properties. Here, we investigate the effect of network heterogeneity on correlations in sparse, random networks of inhibitory neurons with non-linear, conductance-based synapses. Emulations of these networks on the analog neuromorphic hardware system Spikey allow us to test the efficiency of decorrelation by inhibitory feedback in the presence of hardware-specific heterogeneities. The configurability of the hardware substrate enables us to modulate the extent of heterogeneity in a systematic manner. We selectively study the effects of shared input and recurrent connections on correlations in membrane potentials and spike trains. Our results confirm ...

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arXiv2016

Identifying anatomical origins of coexisting oscillations in the cortical microcircuit

Oscillations are omnipresent in neural population signals, like multi-unit recordings, EEG/MEG, and the local field potential. They have been linked to the population firing rate of neurons, with individual neurons firing in a close-to-irregular fashion at low rates. Using a combination of mean-field and linear response theory we predict the spectra generated in a layered microcircuit model of V1, composed of leaky integrate-and-fire neurons and based on connectivity compiled from anatomical and electrophysiological studies. The model exhibits low- and high-gamma oscillations visible in all populations. Since locally generated frequencies are imposed onto other populations, the origin of the oscillations cannot be deduced from the spectra. We develop an universally applicable systematic approach that identifies the anatomical circuits underlying the generation of oscillations in a given network. Based on a theoretical reduction of the dynamics, we derive a sensitivity measure resulting in a frequency-dependent connectivity map that reveals connections crucial for the peak amplitude and frequency of the observed oscillations and identifies the minimal circuit generating a given frequency. The low-gamma peak turns out to be generated in a sub-circuit located in layer 2/3 and 4, while the high-gamma peak emerges from the inter-neurons in layer 4. Connections within and onto layer 5 are found to regulate slow rate fluctuations. We further demonstrate how small perturbations of the crucial connections have significant impact on the population spectra, while the impairment of other connections leaves the dynamics on the population level unaltered. The study uncovers connections where mechanisms controlling the spectra of the cortical microcircuit are most effective.

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arXiv2016

Distributions of covariances as a window into the operational regime of neuronal networks

Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static (quenched) disorder of the connectivity in recurrent random networks was so far elusive. We here derive a finite-size mean-field theory that reduces a disordered to a highly symmetric network with fluctuating auxiliary fields. The exposed analytical relation between the statistics of connections and the statistics of pairwise covariances shows that both, average and dispersion of the latter, diverge at a critical coupling. At this point, a network of nonlinear units transits from regular to chaotic dynamics. Applying these results to recordings from the mammalian brain suggests its operation close to this edge of criticality.

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arXiv2016

Full-density multi-scale account of structure and dynamics of macaque visual cortex

We present a multi-scale spiking network model of all vision-related areas of macaque cortex that represents each area by a full-scale microcircuit with area-specific architecture. The layer- and population-resolved network connectivity integrates axonal tracing data from the CoCoMac database with recent quantitative tracing data, and is systematically refined using dynamical constraints. Simulations reveal a stable asynchronous irregular ground state with heterogeneous activity across areas, layers, and populations. Elicited by large-scale interactions, the model reproduces longer intrinsic time scales in higher compared to early visual areas. Activity propagates down the visual hierarchy, similar to experimental results associated with visual imagery. Cortico-cortical interaction patterns agree well with fMRI resting-state functional connectivity. The model bridges the gap between local and large-scale accounts of cortex, and clarifies how the detailed connectivity of cortex shapes its dynamics on multiple scales.

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arXiv2016

Hybrid scheme for modeling local field potentials from point-neuron networks

Due to rapid advances in multielectrode recording technology, the local field potential (LFP) has again become a popular measure of neuronal activity in both basic research and clinical applications. Proper understanding of the LFP requires detailed mathematical modeling incorporating the anatomical and electrophysiological features of neurons near the recording electrode, as well as synaptic inputs from the entire network. Here we propose a hybrid modeling scheme combining the efficiency of commonly used simplified point-neuron network models with the biophysical principles underlying LFP generation by real neurons. The scheme can be used with an arbitrary number of point-neuron network populations. The LFP predictions rely on populations of network-equivalent, anatomically reconstructed multicompartment neuron models with layer-specific synaptic connectivity. The present scheme allows for a full separation of the network dynamics simulation and LFP generation. For illustration, we apply the scheme to a full-scale cortical network model for a $\sim$1 mm$^2$ patch of primary visual cortex and predict laminar LFPs for different network states, assess the relative LFP contribution from different laminar populations, and investigate the role of synaptic input correlations and neuron density on the LFP. The generic nature of the hybrid scheme and its publicly available implementation in \texttt{hybridLFPy} form the basis for LFP predictions from other point-neuron network models, as well as extensions of the current application to larger circuitry and additional biological detail.

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arXiv2015

A reaction diffusion-like formalism for plastic neural networks reveals dissipative solitons at criticality

Self-organized structures in networks with spike-timing dependent plasticity (STDP) are likely to play a central role for information processing in the brain. In the present study we derive a reaction-diffusion-like formalism for plastic feed-forward networks of nonlinear rate neurons with a correlation sensitive learning rule inspired by and being qualitatively similar to STDP. After obtaining equations that describe the change of the spatial shape of the signal from layer to layer, we derive a criterion for the non-linearity necessary to obtain stable dynamics for arbitrary input. We classify the possible scenarios of signal evolution and find that close to the transition to the unstable regime meta-stable solutions appear. The form of these dissipative solitons is determined analytically and the evolution and interaction of several such coexistent objects is investigated.

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