Sampling Effects on Trajectory Learning and Production

The time-delay neural network (TDNN) and the adaptive time-delay neural network (ATNN) are effective tools for signal production and trajectory generation. Previous studies have shown production of circular and figure-eight trajectories to be robust after training. We show here the effects of different sampling rates on the production of trajectories by the ATNN neural network, including the influence of sampling rate on the robustness and noise-resilience of the resulting system. Although fast training occurred with few samples per trajectory, and the trajectory was learned successfully, more resilience to noise was observed when there were higher numbers of samples per trajectory. The effects of changing the initial segments that begin the trajectory generation were evaluated, and a minimum length of initial segment is required but the location of that segment does not influence the trajectory generation, even when different initial segments are used during training and recall. A major conclusion from these results is that the network learns the inherent features of the trajectory rather than memorizing each point. When a recurrent loop was added from the output to the input of the ATNN, the the training was shown to result in an attractor of the network for a figure-eight trajectory, which involves more complexity due to crossover compared with previous attractor training of a circular trajectory. Furthermore, when the trajectory length was not a multiple of the sampling interval, the trained network generated intervening points on subsequent repetitions of the trajectory, a feature of limit cycle attractors observed in dynamic networks. Thus an effective method of training an individual dynamic attractor into a neural network is extended to more complex trajectories and to show the properties of a limit cycle attractor.