English

On Connected Sublevel Sets in Deep Learning

Machine Learning 2019-05-15 v2 Machine Learning

Abstract

This paper shows that every sublevel set of the loss function of a class of deep over-parameterized neural nets with piecewise linear activation functions is connected and unbounded. This implies that the loss has no bad local valleys and all of its global minima are connected within a unique and potentially very large global valley.

Keywords

Cite

@article{arxiv.1901.07417,
  title  = {On Connected Sublevel Sets in Deep Learning},
  author = {Quynh Nguyen},
  journal= {arXiv preprint arXiv:1901.07417},
  year   = {2019}
}

Comments

Accepted at ICML 2019. More discussions and visualizations are added

R2 v1 2026-06-23T07:18:41.134Z