We introduce a new family of deep neural network models. Instead of specifying a discrete
sequence of hidden layers, we parameterize the derivative of the hidden state using a …

Partial differential equations (PDEs) play a prominent role in many disciplines of science
and engineering. PDEs are commonly derived based on empirical observations. However …

The process of transforming observed data into predictive mathematical models of the
physical world has always been paramount in science and engineering. Although data is …

Recently, deep residual networks have been successfully applied in many computer vision
and natural language processing tasks, pushing the state-of-the-art performance with …

Recent work linking deep neural networks and dynamical systems opened up new avenues
to analyze deep learning. In particular, it is observed that new insights can be obtained by …

Neural networks have been very successful in many applications; we often, however, lack a
theoretical understanding of what the neural networks are actually learning. This problem …

In this paper, we propose a new control framework called the moving endpoint control to
restore images corrupted by different degradation levels in one model. The proposed control …

We present a deep generative model, named Monge-Amp\ere flow, which builds on
continuous-time gradient flow arising from the Monge-Amp\ere equation in optimal transport …

Abstract Residual Networks (ResNets) have become state-of-the-art models in deep
learning and several theoretical studies have been devoted to understanding why ResNet …

During the last few years, significant attention has been paid to the stochastic training of
artificial neural networks, which is known as an effective regularization approach that helps …