Salle U207 - ENS, 29 rue d'Ulm 75005 Paris
Dr. Cristina SAVIN (New York University), Rapporteur
Dr. Jonathan PILLOW (Princeton University), Rapporteur
Dr. Gianluigi MONGILLO (Institute de la Vision), Examinateur
Dr. Alessandro TORCINI (Université de Cergy-Pontoise), Examinateur
Dr. Sophie DENÈVE (École normale supérieure), Directrice de thèse
Dr. Christian MACHENS (Champalimaud Centre for the Unknown), Co-directeur de thèse
The complexity of sensory input is paralleled by the complexity of its representation in the neural activity of biological systems. Starting from the hypothesis that biological networks are tuned to achieve maximal efficiency and robustness, we investigate how efficient representation can be accomplished in networks with experimentally observed local connection probabilities and synaptic dynamics. We develop a Lasso regularized local synaptic rule, which optimizes the number and efficacy of recurrent connections. The connections that impact the efficiency the least are pruned, and the strength of the remaining ones is optimized for efficient signal representation. Our theory predicts that the local connection probability determines the trade-off between the number of population spikes and the number of recurrent synapses, which are developed and maintained in the network. The more sparsely connected networks represent signals with higher firing rates than those with denser connectivity. The variability of observed connection probabilities in biological networks could then be seen as a consequence of this trade-off, and related to different operating conditions of the circuits. The learned recurrent connections are structured, with most connections being reciprocal. The dimensionality of the recurrent weights can be inferred from the network's connection probability and the dimensionality of the feedforward input. The optimal connectivity of a network with synaptic delays is somewhere at an intermediate level, neither too sparse nor too dense. Furthermore, when we add another biological constraint, adaptive regulation of firing rates, our learning rule leads to an experimentally observed scaling of the recurrent weights. Our work supports the notion that biological micro-circuits are highly organized and principled. A detailed examination of the local circuit organization can help us uncover the finer aspects of the principles which govern sensory representation.