We study regularization in the context of small sample-size learning with over-parameterized neural networks. Specifically, we shift focus from architectural properties, such as norms on the network weights, to properties of the internal representations before a linear classifier. Specifically, we impose a topological constraint on samples drawn from the probability measure induced in that space. This provably leads to mass concentration effects around the representations of training instances, i.e., a property beneficial for generalization. By leveraging previous work to impose topological constraints in a neural network setting, we provide empirical evidence (across various vision benchmarks) to support our claim for better generalization.
@article{arxiv.2002.04805,
title = {Topologically Densified Distributions},
author = {Christoph D. Hofer and Florian Graf and Marc Niethammer and Roland Kwitt},
journal= {arXiv preprint arXiv:2002.04805},
year = {2021}
}