论文标题
通过随机初始化训练人工神经网络的强大总体错误分析
Strong overall error analysis for the training of artificial neural networks via random initializations
论文作者
论文摘要
尽管基于深度学习的近似算法已非常成功地应用于许多问题，但目前，从数学的角度来看，其性能的原因尚未完全理解。最近，在深度监督学习的情况下，已经获得了总体误差收敛性的估计，但收敛速度极慢。在本说明中，我们部分改进了这些估计。更具体地说，我们表明，为了获得相同的近似速率，神经网络的深度只需要增加大量速度。在使用I.I.D. \随机初始化的任意随机优化算法的情况下，结果得出。
Although deep learning based approximation algorithms have been applied very successfully to numerous problems, at the moment the reasons for their performance are not entirely understood from a mathematical point of view. Recently, estimates for the convergence of the overall error have been obtained in the situation of deep supervised learning, but with an extremely slow rate of convergence. In this note we partially improve on these estimates. More specifically, we show that the depth of the neural network only needs to increase much slower in order to obtain the same rate of approximation. The results hold in the case of an arbitrary stochastic optimization algorithm with i.i.d.\ random initializations.
