论文标题
用于机器学习自动差异的数学模型
A mathematical model for automatic differentiation in machine learning
论文作者
论文摘要
如今，自动差异化并没有适应现代机器学习需求的简单数学模型。在这项工作中，我们阐明了在实践中实施的程序差异与非平滑函数差异化之间的关系。为此，我们提供了一个简单的功能，一个非平滑的演算，并显示它们如何应用于随机近似方法。我们还证明了由算法分化创造的人为关键点的问题，并显示了通常的方法如何以概率为单位避免这些要点。
Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in practice and differentiation of nonsmooth functions. To this end we provide a simple class of functions, a nonsmooth calculus, and show how they apply to stochastic approximation methods. We also evidence the issue of artificial critical points created by algorithmic differentiation and show how usual methods avoid these points with probability one.
