HOW DELAYS AFFECT NEURAL DYNAMICS AND LEARNING

We investigate the effects of delays on the dynamics and, in particula r, on the oscillatory properties of simple neural network models. We e xtend previously known results regarding. the effects of delays on sta bility and convergence properties. We treat in detail the case of ring networks for which we derive simple conditions for oscillating behavi or and several formulas to predict the regions of bifurcation, the per iods of the limit cycles and the phases of the different neurons. Thes e results in turn can readily be applied to more complex and more biol ogically motivated architectures, such as layered networks. In general , the main result is that delays tend to increase the period of oscill ations and broaden the spectrum of possible frequencies, in a quantifi able way. Simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior. Adapta ble delays are then proposed as one additional mechanism through which neural systems could tailor their own dynamics. Accordingly, we deriv e recurrent back-propagation learning formulas for the adjustment of d elays and other parameters in networks with delayed interactions and d iscuss some possible applications.