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.

翻译：我们利用典型的地形学事实来证明机器学习的分类问题在非常温和的条件下总是可以溶解的。 此外,我们证明软式数学分类网络在输入的地形空间上通过一系列有限的地形学动作来运作,以完成分类任务。此外,考虑到一个培训数据集,我们展示了如何利用地形学形式主义来建议设计为数据分类师培训的神经网络的适当建筑选择。最后,我们展示了神经网络的结构如何不能脱离基本数据的形状而独立选择。为了展示这些结果,我们提供了示例数据集,并展示了神经网如何从这种地形学角度对这些数据采取行动。