On the use of formal methods to model and verify neuronal archetypes  

作　　者：Elisabetta DE MARIA Abdorrahim BAHRAMI Thibaud L'YVONNET Amy FELTY Daniel GAFFÉ Annie RESSOUCHE Franck GRAMMONT 

机构地区：[1]UniversitéCôte d'zur,CNRS,I3S,06903 Sophia Antipolis Cedex,France [2]School of Electrical Engineering and Computer Science,University of Ottawa,Ontario,K1N 6N5,Canada [3]UniversitéCôte d'Azur,INRIA SAM,06902 Sophia Antipolis Cedex,France [4]UniversitéCôte d'Azur,CNRS,LEAT,06903 Sophia Antipolis Cedex,France [5]UniversitéCôte d'Azur,CNRS,LJAD,06108 Nice Cedex 02,France

出　　处：《Frontiers of Computer Science》2022年第3期101-122,共22页中国计算机科学前沿（英文版）

基　　金：This work was supported by the French government through the UCA-Jedi project managed by the National Research Agency(ANR-15-IDEX-01);in particular,by the interdisciplinary Institute for Modeling in Neuroscience and Cognition(NeuroMod)of the UniversitéCôte d'Azur.It was also supported by the Natural Sciences and Engineering Research Council of Canada.

摘　　要：Having a formal model of neural networks can greatly help in understanding and verifying their properties,behavior,and response to external factors such as disease and medicine.In this paper,we adopt a formal model to represent neurons,some neuronal graphs,and their composition.Some specific neuronal graphs are known for having biologically relevant structures and behaviors and we call them archetypes.These archetypes are supposed to be the basis of typical instances of neuronal information processing.In this paper we study six fundamental archetypes(simple series,series with multiple outputs,parallel composition,negative loop,inhibition of a behavior,and contralateral inhibition),and we consider two ways to couple two archetypes:(i)connecting the output(s)of the first archetype to the input(s)of the second archetype and(ii)nesting the first archetype within the second one.We report and compare two key approaches to the formal modeling and verification of the proposed neuronal archetypes and some selected couplings.The first approach exploits the synchronous programming language Lustre to encode archetypes and their couplings,and to express properties concerning their dynamic behavior.These properties are verified thanks to the use of model checkers.The second approach relies on a theorem prover,the Coq Proof Assistant,to prove dynamic properties of neurons and archetypes.

关 键 词：neuronal networks leaky integrate and fire modeling synchronous languages model checking theorem proving LUSTRE COQ formal methods 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]