Neuronal avalanches and learning

Networks of living neurons represent one of the most fascinating systems of biology. If the physical and chemical mechanisms at the basis of the functioning of a single neuron are quite well understood, the collective behaviour of a system of many neurons is an extremely intriguing subject. Crucial ingredient of this complex behaviour is the plasticity property of the network, namely the capacity to adapt and evolve depending on the level of activity. This plastic ability is believed, nowadays, to be at the basis of learning and memory in real brains. Spontaneous neuronal activity has recently shown features in common to other complex systems. Experimental data have, in fact, shown that electrical information propagates in a cortex slice via an avalanche mode. These avalanches are characterized by a power law distribution for the size and duration, features found in other problems in the context of the physics of complex systems and successful models have been developed to describe their behaviour. In this contribution we discuss a statistical mechanical model for the complex activity in a neuronal network. The model implements the main physiological properties of living neurons and is able to reproduce recent experimental results. Then, we discuss the learning abilities of this neuronal network. Learning occurs via plastic adaptation of synaptic strengths by a non-uniform negative feedback mechanism. The system is able to learn all the tested rules, in particular the exclusive OR (XOR) and a random rule with three inputs. The learning dynamics exhibits universal features as function of the strength of plastic adaptation. Any rule could be learned provided that the plastic adaptation is sufficiently slow.