Related papers: A multiscale neural network based on hierarchical …

Depth is the hallmark of deep neural networks. But more depth means more sequential computation and higher latency. This begs the question -- is it possible to build high-performing "non-deep" neural networks? We show that it is. To do so,…

We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…

Deep learning (deep structured learning, hierarchi- cal learning or deep machine learning) is a branch of machine learning based on a set of algorithms that attempt to model high- level abstractions in data by using multiple processing…

Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple…

The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventional kernel-based interpolation techniques. The multi-scale…

We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use…

Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts, including solution of partial differential equations (PDEs). We describe a solver for multiscale fully nonlinear elliptic…

In the field of pattern recognition research, the method of using deep neural networks based on improved computing hardware recently attracted attention because of their superior accuracy compared to conventional methods. Deep neural…

Networks are ubiquitous structure that describes complex relationships between different entities in the real world. As a critical component of prediction task over nodes in networks, learning the feature representation of nodes has become…

Most uses of machine learning today involve training a model from scratch for a particular task, or sometimes starting with a model pretrained on a related task and then fine-tuning on a downstream task. Both approaches offer limited…

This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…

In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…

We introduce a new method based on nonnegative matrix factorization, Neural NMF, for detecting latent hierarchical structure in data. Datasets with hierarchical structure arise in a wide variety of fields, such as document classification,…

Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…

An ability to generalize unconstrained conditions such as severe occlusions and large pose variations remains a challenging goal to achieve in face alignment. In this paper, a multistage model based on deep neural networks is proposed which…

Successful training of convolutional neural networks is often associated with sufficiently deep architectures composed of high amounts of features. These networks typically rely on a variety of regularization and pruning techniques to…

Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large…

In this paper, we investigate the problem of hyperspectral (HS) image spatial super-resolution via deep learning. Particularly, we focus on how to embed the high-dimensional spatial-spectral information of HS images efficiently and…

We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two…

Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that…