Neural Networks and Many-Body Systems

I review one of the papers by Eliano Pessa and myself where we model neural networks as many-body systems. The mathematical formalism underlying the model is here presented. The information input induces the spontaneous breakdown of the SU(2) symmetry of the units of the neural net. The order parameter describes the collective correlation modes propagating over the net and represents the code of the recorded information. The dissipative character of the dynamics allows large memory capacity. Free energy minimization leads to the sigmoid activation function for the neural net units. Entropy and free energy play a crucial role in characterizing the net functional properties.