论文标题
学习神经网络的变分不平等模型
A Variational Inequality Model for Learning Neural Networks
论文作者
论文摘要
神经网络已成为解决信号和图像处理问题的普遍工具，它们通常超过标准方法。然而，在许多应用程序中，培训神经网络是一项具有挑战性的任务。普遍的培训程序包括基于巨大维度的数据集最大程度地减少高度非凸目标。在这种情况下，当前的方法不能保证产生全球解决方案。我们提出了一种替代方法，该方法已经过时了优化框架并采用了各种不平等形式主义。相关的算法保证迭代融合到变异不平等的真实解决方案，并具有有效的块状结构。提出了数值应用。
Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent training procedure consists of minimizing highly non-convex objectives based on data sets of huge dimension. In this context, current methodologies are not guaranteed to produce global solutions. We present an alternative approach which foregoes the optimization framework and adopts a variational inequality formalism. The associated algorithm guarantees convergence of the iterates to a true solution of the variational inequality and it possesses an efficient block-iterative structure. A numerical application is presented.
