P S Neelakanta | PubMed Health

PubMed1993

Stochastical aspects of neuronal dynamics: Fokker-Planck approach.

The stochastical aspects of noise-perturbed neuronal dynamics are studied via the Fokker-Planck equation by considering the Langevin-type relaxational, nonlinear process associated with neuronal states. On the basis of a canonical, stochastically driven, dichotomous state modeling, the equilibrium conditions in the neuronal assembly are analyzed. The markovian structure of the random occurrence of action potentials due to the disturbances (noise) in the neuronal state is considered, and the corresponding solutions relevant to the colored noise spectrum of the disturbance effects are addressed. Stochastical instability (Lyapunov) considerations in solving discrete optimization problems via neural networks are discussed. The bounded estimate(s) of the stochastical variates involved are presented, and the noise-induced perturbations on the saturated-state neuronal population are elucidated.

Action Potentials↗

PubMed1991

Langevin machine: a neural network based on stochastically justifiable sigmoidal function.

In neural networks the activation process controls the output as a nonlinear function of the input; and, this output remains bounded between limits as decided by a logistic function known as the sigmoid (S-shaped). Presently, by applying the considerations of Maxwell-Boltzmann statistics, the Langevin function is shown as the appropriate and justifiable sigmoid (instead of the conventional hyperbolic tangent function) to depict the bipolar nonlinear logic-operation enunciated by the collective stochastical response of artificial neurons under activation. That is, the graded response of a large network of 'neurons' such as Hopfield's can be stochastically justified via the proposed model. The model is consistent with the established link between the Hopfield model and the statistical mechanics. The Langevin function (in lieu of conventional hyperbolic tangent and/or exponential sigmoids) in determining nonlinear decision boundaries, in characterizing the neural networks by the Langevin machine versus the Boltzmann machine, in sharpening and annealing schedules and in the optimization of nonlinear detector performance are discussed.

Animals↗