Brownian motion theory as a physical foundation for feedback neural networks

A stochastic physical model is proposed for a certain class of neurocomputational architectures. The present study is based on considering the potentials of each neuron as a fluctuating quantity. In describing this process, a fluctuation can be understood, in a thermodynamic framework, if one considers the behavior of the variables (the neural potentials in this model) in a system with different types of interaction with the rest of the universe. If this interaction is measured by a temperature T (with the system submerged in a thermic bath), by making T → 0 one obtains an equilibrium system where the dynamic variables do not change through time. Since a macroscopic configuration corresponds to many microscopic states, the variables involved are not completely stationary, and they vary near the equilibrium state; any fluctuation will tend to that state. If one considers the dynamic variables as fluctuations of a subsystem (a neuron) from a closed system (a neural network), one obtains an important physical model since it contains many of the existing phenomena of relaxation in many fields of statistical mechanics.