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Simulation of Large Scale Neural Models with Event-Driven Connectivity Generation Nathalie Azevedo Carvalho, Sylvain Contassot-Vivier, Laure Buhry, Dominique Martinez

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Simulation of Large Scale Neural Models with Event-Driven Connectivity Generation Nathalie Azevedo Carvalho, Sylvain Contassot-Vivier, Laure Buhry, Dominique Martinez Simulation of Large Scale Neural Models With Event-Driven Connectivity Generation Nathalie Azevedo Carvalho, Sylvain Contassot-Vivier, Laure Buhry, Dominique Martinez To cite this version: Nathalie Azevedo Carvalho, Sylvain Contassot-Vivier, Laure Buhry, Dominique Martinez. Simulation of Large Scale Neural Models With Event-Driven Connectivity Generation. Frontiers in Neuroinfor- matics, Frontiers, 2020, 14, pp.14. 10.3389/fninf.2020.522000. hal-03041616 HAL Id: hal-03041616 https://hal.archives-ouvertes.fr/hal-03041616 Submitted on 7 Dec 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. ORIGINAL RESEARCH published: 14 October 2020 doi: 10.3389/fninf.2020.522000 Simulation of Large Scale Neural Models With Event-Driven Connectivity Generation Nathalie Azevedo Carvalho 1*, Sylvain Contassot-Vivier 2, Laure Buhry 1 and Dominique Martinez 2 1 Université de Lorraine, CNRS, Inria, LORIA, Nancy, France, 2 Université de Lorraine, CNRS, LORIA, Nancy, France Accurate simulations of brain structures is a major problem in neuroscience. Many works are dedicated to design better models or to develop more efficient simulation schemes. In this paper, we propose a hybrid simulation scheme that combines time-stepping second-order integration of Hodgkin-Huxley (HH) type neurons with event-driven updating of the synaptic currents. As the HH model is a continuous model, there is no explicit spike events. Thus, in order to preserve the accuracy of the integration method, a spike detection algorithm is developed that accurately determines spike times. This approach allows us to regenerate the outgoing connections at each event, thereby avoiding the storage of the connectivity. Consequently, memory consumption is significantly reduced while preserving execution time and accuracy of the simulations, especially the spike times of detailed point neuron models. The efficiency of the method, implemented in the SiReNe software1, is demonstrated by the simulation of a striatum model which consists of more than 106 neurons and 108 synapses (each neuron has a Edited by: fan-out of 504 post-synaptic neurons), under normal and Parkinson’s conditions. Andrew P. Davison, UMR9197 Institut des Neurosciences Keywords: brain simulation, Hodgkin-Huxley neurons, time-stepping method, event-driven connectivity Paris Saclay (Neuro-PSI), France generation, Runge-Kutta method, Parkinson’s disease, large scale networks Reviewed by: Sandra Diaz Pier, Helmholtz Association of German 1. INTRODUCTION Research Centers (HZ), Germany Petru¸tAntoniu Bogdan, Major projects such as Blue Brain (Markram, 2006), the Human Brain Project (Einevoll et al., 2019), The University of Manchester, the BRAIN Initiative or Mindscope (Hawrylycz et al., 2016), aim at simulating a brain or brain United Kingdom structures. The simulation of brain structures demands not only computing resources but also a *Correspondence: lot of memory to store the connectivity that grows as the power 1.4 of the number of neurons (see Nathalie Azevedo Carvalho Figure 1). Then, the simulation of the human brain would require ≈ 100 terabytes just for storing [email protected] the Boolean connectivity pattern (connection/no connection). Therefore, large-scale simulations of realistic cortical networks have been undertaken by using supercomputers with huge memory Received: 20 December 2019 Accepted: 31 August 2020 space (Izhikevich and Edelman, 2008; Migliore et al., 2006; Chatzikonstantis et al., 2019; Eliasmith Published: 14 October 2020 and Trujillo, 2014). Here, we propose a hybrid approach that combines a time-stepping approach for the numerical Citation: Azevedo Carvalho N, part of the simulation with an event-driven updating of the synaptic currents for complex Hodgkin- Contassot-Vivier S, Buhry L and Huxley (HH) type neurons. This approach is particularly well-suited to studies of real-time Martinez D (2020) Simulation of Large neural mechanisms requiring high accuracy, such as pathological behaviors like the Parkinson’s Scale Neural Models With disease. Our event-driven approach completely avoids the storage of the connectivity pattern by Event-Driven Connectivity Generation. regenerating the connectivity on the fly, when needed, after spiking events. This event-driven Front. Neuroinform. 14:522000. doi: 10.3389/fninf.2020.522000 1Source code is available at: https://sirene.gitlabpages.inria.fr/sirene. Frontiers in Neuroinformatics | www.frontiersin.org 1 October 2020 | Volume 14 | Article 522000 Azevedo Carvalho et al. Simulation With On-Demand Connectivity Generation 1.4 FIGURE 1 | Number of synapses Ns vs. number of neurons Nn for different animal species (vertebrates and invertebrates). The best fit is for the power law Ns = Nn 2 (red line) and not for Ns = Nn (black line), as claimed in Lansner and Diesmann (2012), or the full connectivity Ns = Nn (blue line). All fits are consistent in the sense that Ns = 0 for Nn = 0. generation of the connectivity makes use of pseudo-random methods used in our neural simulator are presented in section 3. generators and consistent seeds. The exact computation of spike Then, validation and performance analysis are provided in times is not possible for HH neurons because the model is section 4. Section 5 draws a general conclusion and proposes a continuous and the membrane voltage is approximated by time- list of future works. stepping methods on discrete time (Koch and Segev, 1998). Moreover, when the membrane potential crosses threshold twice 2. RELATED WORKS during one time-step (the first crossing is upward and the second one is downward), the spike may be missed. A failure to detect a 2.1. Event-Driven Connectivity Generation spiking event may cause dramatic changes on the behavior of the In neuroscience studies, one often simulates a snapshot of a system, especially in the case of event-driven connectivity. network over a short period of time with fixed parameters, e.g., In this paper, we consider an event-driven connectivity for comparing normal vs. pathological neural configurations. generation within time-stepping schemes of Runge-Kutta 2 In such a context, the causal mechanisms (e.g., plasticity midpoint type. We develop a spike detection method for mechanisms) of neural evolution from normal to pathological HH neurons, that accurately determines the spike timings so states is not relevant. Thereby, connectivity storage is not that the accuracy of the second-order Runge-Kutta methods mandatory and can be advantageously replaced by dynamic (RK2) is preserved when connectivity is generated at spiking generation. Originally, the idea of event-driven connectivity events. By avoiding the connectivity storage, our method is generation has been proposed in the case of abstract neurons intended to simulate large-scale models made of Hodgkin- for which spike timing is exactly known, i.e., rule-based artificial Huxley type neurons on a single computing node. Indeed, cell units, or finite state machines (Lytton and Stewart, 2006). the limited memory consumption pushes back the necessity to This approach has then been applied with integrate-and-fire use multiple machines, whose induced communications often (IF) neurons, i.e., quadratic IF (Izhikevich and Edelman, 2008) reduce the overall performance. Yet, computing performance and leaky IF over GPU hardware (Knight and Nowotny, is not neglected in our approach as a parallel multi-threaded 2020). version has been developed in order to take advantage of multi- To the best of our knowledge, the event-driven connectivity core/many-core machines. generation approach has never been developed for Hodgkin- Our approach is implemented in the SiReNe software whose Huxley neurons. Our event-driven connectivity generation accuracy and efficiency are exhibited in a series of experiments makes use of pseudo-random generators and consistent seeds. among which is the simulation of the striatum structure at the rat The principle of pseudo-randomly generating the connectivity scale, i.e., with more than 106 neurons. through an event-driven approach has been reused in a recent In the next section, we demonstrate the originality and interest US patent (Lipasti et al., 2019). Yet, the LFSR (Linear-Feedback of our approach in respect to related works. The different Shift Register) nature of the pseudo-random number generator Frontiers in Neuroinformatics | www.frontiersin.org 2 October 2020 | Volume 14 | Article 522000 Azevedo Carvalho et al. Simulation With On-Demand Connectivity Generation (PRNG) used in their approach is not statistically strong as it does not pass classical linear tests provided in TestU01 Algorithm 1: Simulation scheme (L’Ecuyer and Simard, 2007) which is a reference in the 1 foreach time step t do domain. Moreover, a single PRNG is used to perform all 2 Update the neurons states according to their internal the dynamic data generations, leading to additional time and state and input currents at time t memory consumption. 3 Detect spiking neurons 4 foreach spiking neuron do 5 Update its post-synaptic currents for time t + t
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