Related papers: Stacked tensorial neural networks for reduced-orde…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

Deep neural networks (DNNs) have delivered a remarkable performance in many tasks of computer vision. However, over-parameterized representations of popular architectures dramatically increase their computational complexity and storage…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…

It has been proven that transfer learning provides an easy way to achieve state-of-the-art accuracies on several vision tasks by training a simple classifier on top of features obtained from pre-trained neural networks. The goal of this…

Recent progress in semantic segmentation has been driven by improving the spatial resolution under Fully Convolutional Networks (FCNs). To address this problem, we propose a Stacked Deconvolutional Network (SDN) for semantic segmentation.…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

The deep network model, with the majority built on neural networks, has been proved to be a powerful framework to represent complex data for high performance machine learning. In recent years, more and more studies turn to nonneural network…

Stacking-based deep neural network (S-DNN), in general, denotes a deep neural network (DNN) resemblance in terms of its very deep, feedforward network architecture. The typical S-DNN aggregates a variable number of individually learnable…

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…

Kernel methods are powerful tools to capture nonlinear patterns behind data. They implicitly learn high (even infinite) dimensional nonlinear features in the Reproducing Kernel Hilbert Space (RKHS) while making the computation tractable by…

Stacking-based deep neural network (S-DNN) is aggregated with pluralities of basic learning modules, one after another, to synthesize a deep neural network (DNN) alternative for pattern classification. Contrary to the DNNs trained end to…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

Modern Convolutional Neural Networks (CNN) are extremely powerful on a range of computer vision tasks. However, their performance may degrade when the data is characterised by large intra-class variability caused by spatial transformations.…

We develop a data-driven machine learning approach to identifying parameters with steady-state solutions, locating such solutions, and determining their linear stability for systems of ordinary differential equations and dynamical systems…

A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…

We present Shape-Tailored Deep Neural Networks (ST-DNN). ST-DNN extend convolutional networks (CNN), which aggregate data from fixed shape (square) neighborhoods, to compute descriptors defined on arbitrarily shaped regions. This is natural…

This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…

Conditional computation for Deep Neural Networks (DNNs) reduce overall computational load and improve model accuracy by running a subset of the network. In this work, we present a runtime throttleable neural network (TNN) that can…

Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…