论文标题
深度学习的拓扑框架
A Topological Framework for Deep Learning
论文作者
论文摘要
我们利用拓扑的经典事实来表明机器学习中的分类问题在非常轻微的条件下总是可以解决的。此外，我们表明，软马克斯分类网络通过有限的拓扑移动序列来实现输入拓扑空间，以实现分类任务。此外，鉴于培训数据集，我们展示了如何使用拓扑形式主义为旨在培训作为数据分类器培训的神经网络的适当建筑选择。最后，我们展示了如何不能独立于基础数据的形状选择神经网络的体系结构。为了证明这些结果，我们提供了示例数据集，并从这种拓扑角度展示了神经网的作用。
We utilize classical facts from topology to show that the classification problem in machine learning is always solvable under very mild conditions. Furthermore, we show that a softmax classification network acts on an input topological space by a finite sequence of topological moves to achieve the classification task. Moreover, given a training dataset, we show how topological formalism can be used to suggest the appropriate architectural choices for neural networks designed to be trained as classifiers on the data. Finally, we show how the architecture of a neural network cannot be chosen independently from the shape of the underlying data. To demonstrate these results, we provide example datasets and show how they are acted upon by neural nets from this topological perspective.
