Noisy Neural Net States and Their Time Evolution
Jonathan Taylor · SIAM Journal on Applied Mathematics · 1990
Analysis of suitable definitions of states and their probabilities is given for neural nets in which probabilistic aspects of firing activity are incorporated; probabilities for individual neuronal activity are found most appropriate. Discrete time evolution is modelled most simply by polynomial maps with coefficients given by synaptic parameters. Evolution in continuous time is modelled in a similar fashion. On computer simulation of the discrete-time case the resulting behaviour is found to be convergence to a single fixed point for small nets. Implications of this are briefly discussed.