Information dynamics of neural networks with the aid of supersymmetry fields as the microscopic thermal flow
Yoshitake Yamazaki · Journal of Physics A Mathematical and General · 2000
Information dynamics is discussed from the point of view of microscopic thermal flow. In the fields of learning, association, storage and so on, the concepts of neural networks (NNWs) have been widely used. Their neurodynamics have been investigated as a stochastic process of an infinite neuron system, using the replica method. This approach includes unsettled points; regimes where replica symmetry (RS) solutions and replica symmetry breaking (RSB) solutions are valid, low-dimensional behaviour regimes, and so forth. First, to make them clear, using supersymmetry (SUSY) fields the dynamics of NNWs are investigated for a family of NNWs interacting among m neurons. The dynamics of the system are supposed to be specified according to the Langevin dynamics with Gaussian white noise (i.e. a random influence from the surroundings) under an environmental parameter β (such as the inverse temperature). The results obtained without ambiguity are as follows: the RS solutions are valid in the regime where our solutions satisfy the fluctuation-dissipation theorem (FDT), while the RSB solutions appear in the SUSY-breaking regime. As a function of the environmental parameter, the system displays transitions from usual (ergodic) phases to phases with broken ergodicity. Secondly, the information dynamics of NNW is derived as the microscopic thermal flow.