Interpretable global minima of deep ReLU neural networks on sequentially separable data

no code implementations • 11 May 2024 • Thomas Chen, Patricia Muñoz Ewald

We explicitly construct zero loss neural network classifiers.

Non-approximability of constructive global $\mathcal{L}^2$ minimizers by gradient descent in Deep Learning

no code implementations • 13 Nov 2023 • Thomas Chen, Patricia Muñoz Ewald

We analyze geometric aspects of the gradient descent algorithm in Deep Learning (DL) networks.

Geometric structure of Deep Learning networks and construction of global ${\mathcal L}^2$ minimizers

no code implementations • 19 Sep 2023 • Thomas Chen, Patricia Muñoz Ewald

In this paper, we explicitly determine local and global minimizers of the $\mathcal{L}^2$ cost function in underparametrized Deep Learning (DL) networks; our main goal is to shed light on their geometric structure and properties.

Geometric structure of shallow neural networks and constructive ${\mathcal L}^2$ cost minimization

no code implementations • 19 Sep 2023 • Thomas Chen, Patricia Muñoz Ewald

In this paper, we approach the problem of cost (loss) minimization in underparametrized shallow neural networks through the explicit construction of upper bounds, without any use of gradient descent.