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Section: New Results
Study of Temporal Properties of Neuronal Archetypes
Participants : Annie Ressouche, Daniel Gaffé, Cedric Girard-Riboulleau.
Keywords: biologic archetypes, Leaky Integrate and Fire Modeling, Model Coupling, Neural Spiking networks, Synchronous Languages, Model Checking Synchronous Modeling, model-checking, lustre, temporal logic, probabilistic models, network reduction.
Last year, we began a collaboration with the I3S CNRS laboratory and Jean Dieudonné CNRS laboratory to verify temporal properties of neuronal archetypes. There exist many ways to connect two, three or more neurons together to form different graphs. We call archetypes only the graphs whose properties can be associated with specific classes of biologically relevant structures and behaviors. These archetypes are supposed to be the basis of typical instances of neuronal information processing. To model these different representative archetypes and express their temporal properties, we used a synchronous programming language dedicated to reactive systems (Lustre). Then, we generated several back ends to interface different model checkers supporting data types and automatically validate these properties. We compared the respective results, that mainly depend on the underlying abstraction methods used in model checkers [63].
This year, during the internship of Thibaud l'Yvonnet (funded by the NeuComp project (C@UCA), in which the Stars team is involved.) we tackle the next logical step and proceed to the study of the properties of their couplings. For this purpose, we rely on Leaky Integrate and Fire neuron modeling and we use the synchronous programming language Lustre to implement the neuronal archetypes and to formalize their expected properties. Then, we exploit an associated model checker called kind2 to automatically validate these behaviors. We show that when the archetypes are coupled either these behaviors are slightly modulated or they give way to a brand new behavior. We can also observe that different archetype couplings can give rise to strictly identical behaviors. Our results show that time coding modeling is more suited than rate coding modeling for this kind of studies. These results are published in [30].
On the other hand, in the framework of Cedric Girard Riboulleau internship, we formalize Boolean Probabilistic Leaky Integrate and Fire Neural Networks as Discrete-Time Markov Chains using the language PRISM. In our models, the probability for neurons to emit spikes is driven by the difference between their membrane potential and their firing threshold. The potential value of each neuron is computed taking into account both the current input signals and the past potential values. Taking advantage of this modeling, we propose a novel algorithm which aims at reducing the number of neurons and synaptical connections of a given network. The reduction preserves the desired dynamical behavior of the network, which is formalized by means of temporal logic formulas and verified thanks to the PRISM model checker.