The Lizorkin space is well suited to the study of operators like fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. In return, we show that it is dense in C0(Double- ...
We consider distributed optimization over several devices, each sending incremental model updates to a central server. This setting is considered, for instance, in federated learning. Various schemes have been designed to compress the model updates in orde ...
We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. This classical framework allows us to present the backstepping method with Fredholm transformations for the Lapla ...
When learning from data, leveraging the symmetries of the domain the data lies on is a principled way to combat the curse of dimensionality: it constrains the set of functions to learn from. It is more data efficient than augmentation and gives a generaliz ...
Sign-based algorithms (e.g. signSGD) have been proposed as a biased gradient compression technique to alleviate the communication bottleneck in training large neural networks across multiple workers. We show simple convex counter-examples where signSGD doe ...
Traditional sampling involves encoding a signal through (time, value)-pairs. In contrast, time encoding machines (TEMs) characterize a signal by recording time points which depend on the integral of the signal over time. We study multi-channel TEMs where c ...
The paper introduces a functional time series (lagged) regression model. The impulse-response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L-2 in applications. A spectral approach to the estima ...
Demand has emerged for next generation visual technologies that go beyond conventional 2D imaging. Such technologies should capture and communicate all perceptually relevant three-dimensional information about an environment to a distant observer, providin ...
