초록 ▼

A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifical

A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically, it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved, but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. The trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

대표청구항 ▼

[ What is claimed is:] [1.] A method of training a neural network so that a neuron output state vector thereof obeys a set of forward sensitivity equations over a finite learning period, said method comprising:defining first and auxiliary adjoint systems of equations governing an adjoint function an

[ What is claimed is:] [1.] A method of training a neural network so that a neuron output state vector thereof obeys a set of forward sensitivity equations over a finite learning period, said method comprising:defining first and auxiliary adjoint systems of equations governing an adjoint function and an auxiliary adjoint function, respectively, of said neural network;setting said adjoint function to zero at the beginning of said learning period and integrating said adjoint system of equations forward in time over said learning period to produce a first term of an indirect effect of a sensitivity gradient of said neural network;setting said auxiliary adjoint function to zero at the end of said learning period and integrating said auxiliary adjoint system of equations forward in time over said learning period to produce a remaining term of said indirect effect;computing a sum of said first and remaining terms, and multiplying said sum by a learning rate; andsubtracting the product thereof from a current neuron parameter vector to produce an updated neuron parameter vector.