On the Analysis of Sigmoid Time Parameters for Dynamic Truncated BPTT Algorithm

The purpose of the research addressed in this paper concerns a comparative study of two expressions of the time scale parameter for continuous time recurrent neural network (CTRNN): a classical time constant expression, and a sigmoid one. Their influence on the stability, the convergence speed and the generalization ability of a Backpropagation through time (BPTT) learning algorithm, will be discussed. Firstly, three mathematical conclusions related to the propagation and learning equations are deduced. Then these conclusions are validated on experiments carried out on a real biped robot. Through the identification of the balancing behavior under different robot torso motions, the sigmoid expression will be shown to get the best learning results.