On the Topological Expressive Power of Neural Networks

Abstract

We propose a topological description of neural network expressive power. We adopt the topology of the space of decision boundaries realized by a neural architecture as a measure of its intrinsic expressive power. By sampling a large number of neural architectures with different sizes and design, we show how such measure of expressive power depends on the properties of the architectures, like depth, width and other related quantities.

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Cite

Text

Petri and Leitão. "On the Topological Expressive Power of Neural Networks." NeurIPS 2020 Workshops: TDA_and_Beyond, 2020.

Markdown

[Petri and Leitão. "On the Topological Expressive Power of Neural Networks." NeurIPS 2020 Workshops: TDA_and_Beyond, 2020.](https://mlanthology.org/neuripsw/2020/petri2020neuripsw-topological/)

BibTeX

@inproceedings{petri2020neuripsw-topological,
  title     = {{On the Topological Expressive Power of Neural Networks}},
  author    = {Petri, Giovanni and Leitão, António},
  booktitle = {NeurIPS 2020 Workshops: TDA_and_Beyond},
  year      = {2020},
  url       = {https://mlanthology.org/neuripsw/2020/petri2020neuripsw-topological/}
}