Diyora Salimova

Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions

This paper shows that the infimum of the loss is always zero and achievable with at least $d$ active and visible hidden neurons -- that is, hidden neurons with non-zero inner and outer weights -- with pairwise distinct pivots, and provides for arbitrary activation degree $d$ a sharp existence/non-existence criterion for global minimizers with necessary structural conditions.