7 papers
Explicit neural network classifiers for non-separable data
Patrícia Muñoz Ewald
We fully characterize a large class of feedforward neural networks in terms of truncation maps. As an application, we show how a ReLU neural network can implement a feature map whi…
Architecture independent generalization bounds for overparametrized deep ReLU networks
Anandatheertha Bapu, Thomas Chen, Chun-Kai Kevin Chien +2
We prove that overparametrized neural networks are able to generalize with a test error that is independent of the level of overparametrization, and independent of the Vapnik-Cherv…
Gradient flow in parameter space is equivalent to linear interpolation in output space
Thomas Chen, Patrícia Muñoz Ewald
We prove that the standard gradient flow in parameter space that underlies many training algorithms in deep learning can be continuously deformed into an adapted gradient flow whic…
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…
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…