Integration of Continuous-Time Dynamics in a Spiking Neural Network Simulator.

Jan Hahne,David Dahmen,Markus Diesmann,Jannis Schuecker,Andreas Frommer,Matthias Bolten,Moritz Helias

doi:10.3389/fninf.2017.00034

Abstract

Contemporary modeling approaches to the dynamics of neural networks include two important classes of models: biologically grounded spiking neuron models and functionally inspired rate-based units. We present a unified simulation framework that supports the combination of the two for multi-scale modeling, enables the quantitative validation of mean-field approaches by spiking network simulations, and provides an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes. While most 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. In addition to the standard implementation we present an iterative approach based on waveform-relaxation techniques to reduce communication and increase performance for large-scale simulations of rate-based models with instantaneous interactions. Finally we 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.

Highlights

IntroductionMultiple strategies of neural network modeling have emerged in computational neuroscience
Over the past decades, multiple strategies of neural network modeling have emerged in computational neuroscience
This work presents an efficient way to integrate rate-based models in a neuronal network simulator that is originally designed for models with delayed spike-based interactions

Summary

Introduction

Multiple strategies of neural network modeling have emerged in computational neuroscience. Inspired top-down approaches that aim to understand computation in neural networks typically describe neurons or neuronal populations in terms of continuous variables, e.g., firing rates (Hertz et al, 1991; Schöner et al, 2015). Rate-based models originate from the seminal works by Wilson and Cowan (1972) and Amari (1977) and were introduced as a coarse-grained description of the overall activity of large-scale neuronal. Being amenable to mathematical analysis and exhibiting rich dynamics such as multistability, oscillations, traveling waves, and spatial patterns (see e.g., Roxin et al, 2005), rate-based models have fostered progress in the understanding of memory, sensory and motor processes including visuospatial working memory, decision making, perceptual rivalry, geometric visual hallucination patterns, ocular dominance and orientation selectivity, spatial navigation, and movement preparation (reviewed in Coombes, 2005; Bressloff, 2012; Kilpatrick, 2015). Ideas from functional network models have further inspired the field of artificial neuronal networks in the domain of engineering (Haykin, 2009)

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