6 papers
Interpretable global minima of deep ReLU neural networks on sequentially separable data
Thomas Chen, Patrícia Muñoz Ewald
We explicitly construct zero loss neural network classifiers. We write the weight matrices and bias vectors in terms of cumulative parameters, which determine truncation maps actin…
Global minimization at uniform exponential rate via geometrically adapted gradient descent in Deep Learning
Thomas Chen
We consider the scenario of supervised learning in Deep Learning (DL) networks, and exploit the arbitrariness of choice in the Riemannian metric relative to which the gradient desc…
On non-approximability of zero loss global minimizers by gradient descent in Deep Learning
Thomas Chen, Patricia Muñoz Ewald
We analyze geometric aspects of the gradient descent algorithm in Deep Learning (DL), and give a detailed discussion of the circumstance that in underparametrized DL networks, zero…
Geometric structure of Deep Learning networks and construction of global minimizers
Thomas Chen, Patricia Muñoz Ewald
In this paper, we explicitly determine local and global minimizers of the cost function in underparametrized Deep Learning (DL) networks; our main goal is to shed l…
Geometric structure of shallow neural networks and constructive cost minimization
Thomas Chen, Patrícia Muñoz Ewald
In this paper, we approach the problem of cost (loss) minimization in underparametrized shallow ReLU networks through the explicit construction of upper bounds which appeal to the…
On the Well-posedness and Stability of Cubic and Quintic Nonlinear Schrödinger Systems on
Thomas Chen, Amie Urban
In this paper, we study cubic and quintic nonlinear Schrödinger systems on 3-dimensional tori, with initial data in an adapted Hilbert space and all of our res…