Related papers: Tensor-based Nonlinear Classifier for High-Order D…

This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank…

CNNs achieve remarkable performance by leveraging deep, over-parametrized architectures, trained on large datasets. However, they have limited generalization ability to data outside the training domain, and a lack of robustness to noise and…

Self-attentive transformer models have recently been shown to solve the next item recommendation task very efficiently. The learned attention weights capture sequential dynamics in user behavior and generalize well. Motivated by the special…

Higher-order data with high dimensionality is of immense importance in many areas of machine learning, computer vision, and video analytics. Multidimensional arrays (commonly referred to as tensors) are used for arranging higher-order data…

In this paper, we study novel neural network structures to better model long term dependency in sequential data. We propose to use more memory units to keep track of more preceding states in recurrent neural networks (RNNs), which are all…

Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…

The interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used…

Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…

We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new…

We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…

Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…

Recurrent Neural Network (RNN) are a popular choice for modeling temporal and sequential tasks and achieve many state-of-the-art performance on various complex problems. However, most of the state-of-the-art RNNs have millions of parameters…

Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have…

In this work, we firstly apply the Train-Tensor (TT) networks to construct a compact representation of the classical Multilayer Perceptron, representing a reduction of up to 95% of the coefficients. A comparative analysis between tensor…

Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either…

We study the impact of neural networks in text classification. Our focus is on training deep neural networks with proper weight initialization and greedy layer-wise pretraining. Results are compared with 1-layer neural networks and Support…

The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…

We introduce highly efficient online nonlinear regression algorithms that are suitable for real life applications. We process the data in a truly online manner such that no storage is needed, i.e., the data is discarded after being used.…

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…

This paper presents a novel online learning method that aims at finding a separator hyperplane between data points labelled as either positive or negative. Since weights and biases of artificial neurons can directly be related to…