## Section: New Results

### Spiking neurons

Participants : Hana Belmabrouk, Dominique Martinez, Thierry Viéville, Thomas Voegtlin.

#### Mathematical modeling

In order to understand the dynamics of spiking neural networks under the influence of a modified synaptic dynamics of single neurons, we study the effect of tonic inhibition on the population activity in spiking neural networks. The aim is to derive mathematical relations of the population activity and some statistics estimated numerically from the simulation of networks [4] , [8] .

#### 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 have studied new aspects of our models of the insect olfactory system [7] , [14] .

#### Using event-based metric for event-based neural network weight adjustment

The problem of adjusting the parameters of an event-based network model is addressed here at the programmatic level. Considering temporal processing, the goal is to adjust the network units weights so that the outcoming events correspond to what is desired. The work of [18] proposes, in the deterministic and discrete case, a way to adapt usual alignment metrics in order to derive suitable adjustment rules. At the numerical level, the stability and unbiasness of the method is verified.

The key point, here, is the non-learnability of even-based ,
since it is proved that this problem is NP-complete, when considering
the estimation of both weights in the general case,
except for exact simulation.
We show that we can “elude” this caveat and propose an alternate
efficient estimation mechanism,
inspired by alignment metrics used in spike train analysis,
thus providing a complement of other estimation approaches,
beyond usual convolution metric.
At last, the proposed mollification *is* a series of convolution
metric,
but that converges towards the expected alignment metric.

#### Predictive learning

In collaboration with Sander Bohte (CWI, Netherlands) and Nicolas Fourcaud-Trocme (CNRS, Lyon), we are developing a model of predictive learning using oscillations in a population of spiking neurons. The model is based on previous work performed in the Cortex group. Our previous model suggested a possible role for neuronal synchronization in unsupervised, predictive-type learning. However, that model was not compatible with sustained oscillations observed in biological networks. We are extending our initial approach in order to allow the network to learn during a stable, steady-state oscillatory regime. This extension involves using type-2 neurons and two distinct types of inhibition.