相关论文: A multiscale neural network based on hierarchical …

We introduce the Hierarchically Interacting Particle Neural Network (HIP-NN) to model molecular properties from datasets of quantum calculations. Inspired by a many-body expansion, HIP-NN decomposes properties, such as energy, as a sum over…

We propose to employ the hierarchical coarse-grained structure in the artificial neural networks explicitly to improve the interpretability without degrading performance. The idea has been applied in two situations. One is a neural network…

Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availability of high-performance computing infrastructure, many…

Based on the property that solving the system of linear matrix equations via the column space and the row space projections boils down to an approximation in the least squares error sense, a formulation for learning the weight matrices of…

The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…

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…

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…

We present MR-Net, a general architecture for multiresolution neural networks, and a framework for imaging applications based on this architecture. Our coordinate-based networks are continuous both in space and in scale as they are composed…

Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…

Hierarchical structures exist in both linguistics and Natural Language Processing (NLP) tasks. How to design RNNs to learn hierarchical representations of natural languages remains a long-standing challenge. In this paper, we define two…

Neural Networks sequentially build high-level features through their successive layers. We propose here a new neural network model where each layer is associated with a set of candidate mappings. When an input is processed, at each layer,…

Traditional neural networks (multi-layer perceptrons) have become an important tool in data science due to their success across a wide range of tasks. However, their performance is sometimes unsatisfactory, and they often require a large…

A large amount of research on Convolutional Neural Networks has focused on flat Classification in the multi-class domain. In the real world, many problems are naturally expressed as problems of hierarchical classification, in which the…

In this paper, we introduce a type of tensor neural network based machine learning method to solve elliptic multiscale problems. Based on the special structure, we can do the direct and highly accurate high dimensional integrations for the…

We present a new kernel-based algorithm for modeling evenly distributed multidimensional datasets that does not rely on input space sparsification. The presented method reorganizes the typical single-layer kernel-based model into a deep…

We present a new distributed representation in deep neural nets wherein the information is represented in native form as a matrix. This differs from current neural architectures that rely on vector representations. We consider matrices as…

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…

Because hyperspectral remote sensing images contain a lot of redundant information and the data structure is highly non-linear, leading to low classification accuracy of traditional machine learning methods. The latest research shows that…

We present a novel Deep Neural Network (DNN) architecture for non-linear system identification. We foster generalization by constraining DNN representational power. To do so, inspired by fading memory systems, we introduce inductive bias…

Statistical analysis of massive datasets very often implies expensive linear algebra operations with large dense matrices. Typical tasks are an estimation of unknown parameters of the underlying statistical model and prediction of missing…