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Deep Convolutional Neural Networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful…
The performance of Feedforward neural network (FNN) fully de-pends upon the selection of architecture and training algorithm. FNN architecture can be tweaked using several parameters, such as the number of hidden layers, number of hidden…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
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…
We propose a new method, Patch-CNN, for diffusion tensor (DT) estimation from only six-direction diffusion weighted images (DWI). Deep learning-based methods have been recently proposed for dMRI parameter estimation, using either voxel-wise…
Inspired by the ConvNets with structured hidden representations, we propose a Tensor-based Neural Network, TCNN. Different from ConvNets, TCNNs are composed of structured neurons rather than scalar neurons, and the basic operation is neuron…
This study investigates the layerwise importance of feed-forward networks (FFNs) in Transformer-based language models during pretraining. We introduce an experimental approach that, while maintaining the total parameter count, increases the…
Feed-forward neural networks are a novel class of variational wave functions for correlated many-body quantum systems. Here, we propose a specific neural network ansatz suitable for systems with real-valued wave functions. Its…
Binary Convolutional Neural Networks (CNNs) can significantly reduce the number of arithmetic operations and the size of memory storage, which makes the deployment of CNNs on mobile or embedded systems more promising. However, the accuracy…
This paper quantitatively characterizes the approximation power of deep feed-forward neural networks (FNNs) in terms of the number of neurons. It is shown by construction that ReLU FNNs with width $\mathcal{O}\big(\max\{d\lfloor…
Neural network models generally involve two important components, i.e., network architecture and neuron model. Although there are abundant studies about network architectures, only a few neuron models have been developed, such as the MP…
We provide novel guaranteed approaches for training feedforward neural networks with sparse connectivity. We leverage on the techniques developed previously for learning linear networks and show that they can also be effectively adopted to…
Convolutional Neural Networks (CNNs) excel at extracting local features hierarchically, but their performance in capturing complex correlations hinges heavily on deep architectures, which are usually computationally demanding and difficult…
The single-layer feedforward neural network with random weights is a recurring motif in the neural networks literature. The advantage of these networks is their simplified training, which reduces to solving a ridge-regression problem. A…
The first provably efficient algorithm for learning graph neural networks (GNNs) with one hidden layer for node information convolution is provided in this paper. Two types of GNNs are investigated, depending on whether labels are attached…
We study the approximation of functions by tensor networks (TNs). We show that Lebesgue $L^p$-spaces in one dimension can be identified with tensor product spaces of arbitrary order through tensorization. We use this tensor product…
In this paper, we explore different ways to extend a recurrent neural network (RNN) to a \textit{deep} RNN. We start by arguing that the concept of depth in an RNN is not as clear as it is in feedforward neural networks. By carefully…
Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…
Hypergraph neural networks (HGNN) have recently become attractive and received significant attention due to their excellent performance in various domains. However, most existing HGNNs rely on first-order approximations of hypergraph…
Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires…