The dynamics of neural codes in biological and artificial neural networks : from criticality to machine learning and drifting representations

Résumé

In this thesis, we will combine three different approaches to the study of the dynamics of neural networks and their encoding representations: a computational approach, that builds upon basic biological features of neurons and their networks to construct effective models that can simulate their structure and dynamics; a machine-learning approach, which draws a parallel with the functional capabilities of brain networks, allowing us to infer the dynamical and encoding properties required to solve certain inputprocessing tasks; and a final, theoretical treatment, which will take us into the fascinating hypothesis of the “critical” brain as the mathematical foundation that can explain the emergent collective properties arising from the interactions of millions of neurons. Hand in hand with Physics, we will adventure into the realm of neuroscience to explain the existence of quasi-universal scaling properties across brain regions, setting to quantify the distance of their dynamics from a critical point. We will them move into the grounds of artificial intelligence, where the very same theory of critical phenomena will prove very useful to explain the effects of biologically-inspired plasticity rules in the prediction ability of Reservoir Computers. Half-way into our journey, we introduce the concept of neural representations of external stimuli, unveiling a surprising link between the dynamical regime of neural networks and the optimal topological properties of these representation manifolds. The thesis ends with the singular problem of representational drift in the encoding of odors by the olfactory cortex, uncovering the potential synaptic plasticity mechanisms that could explain this recently observed phenomenon.