5 papers
The Barron-Lipschitz Energy Gap and Depth Separation Phenomena in Scientific Machine Learning
Nima Rezaei, Stephan Wojtowytsch
We illustrate in several examples that even neural networks of infinite width (specifically, Barron functions) may encounter substantial obstacles when used as a model class for pr…
Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs
Oluwatosin Akande, Patrick Dondl, Kanan Gupta +2
We study the momentum-based minimization of a diffuse perimeter functional on Euclidean spaces and on graphs with applications to semi-supervised classification tasks in machine le…
Convex-concave splitting for the Allen-Cahn equation leads to -slow movement of interfaces
Patrick Dondl, Akwum Onwunta, Ludwig Striet +1
The convex-concave splitting discretization of the Allen-Cahn is easy to implement and guaranteed to be energy decreasing even for large time-steps. We analyze the time-stepping sc…
Nesterov acceleration in benignly non-convex landscapes
Kanan Gupta, Stephan Wojtowytsch
While momentum-based optimization algorithms are commonly used in the notoriously non-convex optimization problems of deep learning, their analysis has historically been restricted…
Nesterov acceleration despite very noisy gradients
Kanan Gupta, Jonathan W. Siegel, Stephan Wojtowytsch
We present a generalization of Nesterov's accelerated gradient descent algorithm. Our algorithm (AGNES) provably achieves acceleration for smooth convex and strongly convex minimiz…