Section: New Results

Spiking neurons

Participants : Hana Belmabrouk, Yann Boniface, Mohamed-Ghaïth Kaabi, Dominique Martinez, Horacio Rostro, Thierry Viéville, Thomas Voegtlin.

Mathematical modeling

• We demystify some aspects of coding with spike-timing, through a simple review of well-understood technical facts regarding spike coding, allowing to better understand to which extent computing and modeling with spiking neuron networks might be biologically plausible and computationally efficient. Considering a deterministic implementation of spiking neuron networks, we are able to propose results, formula and concrete numerical values, on several topics: (i) general time constraints, (ii) links between continuous signals and spike trains, (iii) spiking neuron networks parameter adjustment. This should prevent one from implementing mechanisms that would be meaningless relative to obvious time constraints, or from artificially introducing spikes when continuous calculations would be sufficient and more simple.

• We propose a generalization of the existing maximum entropy models used for spike train statistics analysis, bringing a simple method to estimate statistics and generalizing existing approaches based on Ising model or one step Markov chains to arbitrary parametric potentials. Our method enables one to take into account memory effects in dynamics. It provides directly the “free-energy” density and the Kullback-Leibler divergence between the empirical statistics and the statistical model. Furthermore, it allows the comparison of different statistical models and offers a control of finite-size sampling effects, inherent to empirical statistics, by using large deviations results. This work is submitted for publication.

• Following some theoretical work about back-engineering from spike recordings, we study the possibility to design an artificial vision system based on spiking neurons, for which neural connections and synaptic weights are directly derived from recordings of spiking activities in the human visual system through a back-engineering approach. A specific simple spiking model has been defined that mathematically enables this back-engineering process from biological data. From a hardware point of view, this model results in an efficient implementation on FPGAs

Biophysical modeling

Our understanding of the computations that take place in the human brain is limited by the extreme complexity of the cortex, and by the difficulty of experimentally recording neural activities, for practical and ethical reasons. The Human Genome Project was preceded by the sequencing of smaller but complete genomes. Similarly, it is likely that future breakthroughs in neuroscience will result from the study of smaller but complete nervous systems, such as the insect brain or the rat olfactory bulb. These relatively small nervous systems exhibit general properties that are also present in humans, such as neural synchronization and network oscillations. Our goal is therefore to understand the role of these phenomena by combining biophysical modelling and experimental recordings, before we can apply this knowledge to humans. In the last year, we obtained the following results :

• We have explored the role of subthreshold membrane potential oscillations in stabilizing the oscillation frequency in a model of the olfactory bulb [9] .

• We have developed several biophysical models of the insect olfactory system to explain the transformation from first-order [10] to second-order neurons [6] , [16] . We show in particular how cellular and network mechanisms contribute to coding efficiency.