Medical imaging is crucial in modern clinics to provide guidance to the diagnosis and
treatment of diseases. Medical image reconstruction is one of the most fundamental and …

As one of the most popular approaches in artificial intelligence, deep learning (DL) has
attracted a lot of attention in the medical physics field over the past few years. The goals of …

Deep learning achieves state-of-the-art results in many tasks in computer vision and natural
language processing. However, recent works have shown that deep networks can be …

We describe the new field of the mathematical analysis of deep learning. This field emerged
around a list of research questions that were not answered within the classical framework of …

The Transformer architecture is widely used in natural language processing. Despite its
success, the design principle of the Transformer remains elusive. In this paper, we provide a …

We build on the dynamical systems approach to deep learning, where deep residual
networks are idealized as continuous-time dynamical systems, from the approximation …

Training deep neural networks with stochastic gradient descent (SGD) can often achieve
zero training loss on real-world tasks although the optimization landscape is known to be …

We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep
learning neural networks have been interpreted as discretisations of an optimal control …

We present a continuous formulation of machine learning, as a problem in the calculus of
variations and differential-integral equations, in the spirit of classical numerical analysis. We …

Over the past few years, deep learning has risen to the foreground as a topic of massive
interest, mainly as a result of successes obtained in solving large-scale image processing …