Related papers: Poly-MgNet: Polynomial Building Blocks in Multigri…

Multiplex networks are complex graph structures in which a set of entities are connected to each other via multiple types of relations, each relation representing a distinct layer. Such graphs are used to investigate many complex…

We present evidence that multigrid (MG) works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder. We introduce a "neural computations" point of view into large scale…

Residual Networks (ResNets) have become state-of-the-art models in deep learning and several theoretical studies have been devoted to understanding why ResNet works so well. One attractive viewpoint on ResNet is that it is optimizing the…

MobileNet and Binary Neural Networks are two among the most widely used techniques to construct deep learning models for performing a variety of tasks on mobile and embedded platforms.In this paper, we present a simple yet efficient scheme…

Despite the remarkable capabilities of deep neural networks in image recognition, the dependence on activation functions remains a largely unexplored area and has yet to be eliminated. On the other hand, Polynomial Networks is a class of…

We extend and analyze the deep neural network multigrid solver (DNN-MG) for the Navier-Stokes equations in three dimensions. The idea of the method is to augment a finite element simulation on coarse grids with fine scale information…

Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in…

Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph…

We present the deep neural network multigrid solver (DNN-MG) that we develop for the instationary Navier-Stokes equations. DNN-MG improves computational efficiency using a judicious combination of a geometric multigrid solver and a…

Existing deep learning approaches for image super-resolution, particularly those based on CNNs and attention mechanisms, often suffer from structural inflexibility. Although graph-based methods offer greater representational adaptability,…

We propose a simple yet effective method to reduce the redundancy of DenseNet by substantially decreasing the number of stacked modules by replacing the original bottleneck by our SMG module, which is augmented by local residual.…

Hypergraph neural networks have been promising tools for handling learning tasks involving higher-order data, with notable applications in web graphs, such as modeling multi-way hyperlink structures and complex user interactions. Yet, their…

We present a novel high frequency residual learning framework, which leads to a highly efficient multi-scale network (MSNet) architecture for mobile and embedded vision problems. The architecture utilizes two networks: a low resolution…

The computational complexity of classical numerical methods for solving Partial Differential Equations (PDE) scales significantly as the resolution increases. As an important example, climate predictions require fine spatio-temporal…

We introduce STAResNet, a ResNet architecture in Spacetime Algebra (STA) to solve Maxwell's partial differential equations (PDEs). Recently, networks in Geometric Algebra (GA) have been demonstrated to be an asset for truly geometric…

Recent advancements in image restoration methods employing global modeling have shown promising results. However, these approaches often incur substantial memory requirements, particularly when processing ultra-high-definition (UHD) images.…

During the last decade, Neural Networks (NNs) have proved to be extremely effective tools in many fields of engineering, including autonomous vehicles, medical diagnosis and search engines, and even in art creation. Indeed, NNs often…

This paper introduces MDP homomorphic networks for deep reinforcement learning. MDP homomorphic networks are neural networks that are equivariant under symmetries in the joint state-action space of an MDP. Current approaches to deep…

Magnetic resonance imaging (MRI) is an essential diagnostic tool that suffers from prolonged scan times. Reconstruction methods can alleviate this limitation by recovering clinically usable images from accelerated acquisitions. In…

Computations over the rational numbers often encounter the problem of intermediate coefficient growth. A solution to this is provided by modular methods, which apply the algorithm under consideration modulo a number of primes and then lift…