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Tensor ring (TR) decomposition is a powerful tool for exploiting the low-rank nature of multiway data and has demonstrated great potential in a variety of important applications. In this paper, nonnegative tensor ring (NTR) decomposition…

Computer Vision and Pattern Recognition · Computer Science 2020-10-13 Yuyuan Yu , Guoxu Zhou , Ning Zheng , Shengli Xie , Qibin Zhao

Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition. We extend these models to the multi-output setting, i.e., for learning vector-valued functions, with application…

Machine Learning · Statistics 2017-11-07 Mathieu Blondel , Vlad Niculae , Takuma Otsuka , Naonori Ueda

Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…

Numerical Analysis · Mathematics 2024-12-20 Longhao Yuan , Chao Li , Jianting Cao , Qibin Zhao

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…

Machine Learning · Computer Science 2026-03-03 Maryam Bagherian

We demonstrate the use of tensor networks for image classification with the TensorNetwork open source library. We explain in detail the encoding of image data into a matrix product state form, and describe how to contract the network in a…

Machine Learning · Computer Science 2019-06-17 Stavros Efthymiou , Jack Hidary , Stefan Leichenauer

Deep neural networks currently demonstrate state-of-the-art performance in several domains. At the same time, models of this class are very demanding in terms of computational resources. In particular, a large amount of memory is required…

Machine Learning · Computer Science 2015-12-22 Alexander Novikov , Dmitry Podoprikhin , Anton Osokin , Dmitry Vetrov

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Machine Learning · Computer Science 2020-05-05 Sandor Szedmak , Anna Cichonska , Heli Julkunen , Tapio Pahikkala , Juho Rousu

In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support vector machines,…

Machine Learning · Computer Science 2017-11-07 Zhongming Chen , Kim Batselier , Johan A. K. Suykens , Ngai Wong

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

Data Structures and Algorithms · Computer Science 2014-01-21 Aditya Bhaskara , Moses Charikar , Ankur Moitra , Aravindan Vijayaraghavan

A fundamental aspect of relational data, such as from a social network, is the possibility of dependence among the relations. In particular, the relations between members of one pair of nodes may have an effect on the relations between…

Methodology · Statistics 2015-11-06 Peter D. Hoff

Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…

Machine Learning · Computer Science 2016-12-30 Sanjeev Arora , Rong Ge , Tengyu Ma , Andrej Risteski

In the context of neural network models, overparametrization refers to the phenomena whereby these models appear to generalize well on the unseen data, even though the number of parameters significantly exceeds the sample sizes, and the…

Machine Learning · Statistics 2020-03-25 Matt Emschwiller , David Gamarnik , Eren C. Kızıldağ , Ilias Zadik

The Recurrent Neural Networks and their variants have shown promising performances in sequence modeling tasks such as Natural Language Processing. These models, however, turn out to be impractical and difficult to train when exposed to very…

Computer Vision and Pattern Recognition · Computer Science 2017-07-07 Yinchong Yang , Denis Krompass , Volker Tresp

Densely connected convolutional networks (DenseNet) behave well in image processing. However, for regression tasks, convolutional DenseNet may lose essential information from independent input features. To tackle this issue, we propose a…

Machine Learning · Computer Science 2022-07-13 Chao Jiang , Canchen Jiang , Dongwei Chen , Fei Hu

Tensor networks have emerged as promising tools for machine learning, inspired by their widespread use as variational ansatze in quantum many-body physics. It is well known that the success of a given tensor network ansatz depends in part…

Quantum Physics · Physics 2022-03-02 Ian Convy , William Huggins , Haoran Liao , K. Birgitta Whaley

Tensor decomposition serves as a powerful primitive in statistics and machine learning, and has numerous applications in problems such as learning latent variable models or mixture of Gaussians. In this paper, we focus on using power…

Machine Learning · Computer Science 2025-03-25 Yuchen Wu , Kangjie Zhou

We present an algorithm for supervised learning using tensor networks, employing a step of preprocessing the data by coarse-graining through a sequence of wavelet transformations. We represent these transformations as a set of tensor…

Machine Learning · Statistics 2020-01-24 Justin Reyes , Miles Stoudenmire

In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a…

Statistics Theory · Mathematics 2017-10-05 Elina Robeva , Anna Seigal

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…

Methodology · Statistics 2021-10-29 Jiaxin Hu , Chanwoo Lee , Miaoyan Wang

We present an extended abstract for the previously published work TESSERACT [Mahajan et al., 2021], which proposes a novel solution for Reinforcement Learning (RL) in large, factored action spaces using tensor decompositions. The goal of…