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Neural network training by integration of adjoint systems of equations forward in time

机译:通过及时整合积分方程组的辅助系统进行神经网络训练

摘要

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.
机译:用于时间依赖轨迹的监督神经学习的方法和设备利用了伴随算子的概念,以使得能够以高效的方式相对于网络架构的各种参数计算目标函数的梯度。具体而言,它结合了伴随方法固有的计算复杂度显着降低的优势,以及能够同时向前求解两个伴随方程组的能力。不仅可以节省大量的计算和存储,而且实时应用程序的处理也变得可能。本发明已经将其应用于两个代表性的复杂度示例,最近在公开文献中对其进行了分析,并证明与文献中报道的12000个相比,圆形轨迹可以大约200次迭代学习。与之前所需的20000次相比,在500次迭代中获得了八字形轨迹。使用我们的新方法计算出的轨迹比以前的研究报告更接近目标轨迹。

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