We study how training molds the Riemannian geometry induced by neural network feature maps. At infinite width, neural networks with random parameters induce highly symmetric metrics on input space. Feature learning in networks trained to perform classification tasks magnifies local areas along decision boundaries. These changes are consistent with previously proposed geometric approaches for hand-tuning of kernel methods to improve generalization.

翻译：我们研究了训练如何塑造由神经网络特征映射诱导的黎曼几何。在无限宽度下，随机参数的神经网络会在输入空间上诱导出高度对称的度量。在训练执行分类任务的网络过程中，特征学习会放大决策边界附近的局部区域。这些变化与先前提出的通过手动调整核方法以改善泛化能力的几何方法一致。