Related papers: Tensor Neural Network and Its Numerical Integratio…

The success of deep neural networks in many real-world applications is leading to new challenges in building more efficient architectures. One effective way of making networks more efficient is neural network compression. We provide an…

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…

Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. Also there is often a gap…

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…

Tensor networks are efficient factorisations of high-dimensional tensors into a network of lower-order tensors. They have been most commonly used to model entanglement in quantum many-body systems and more recently are witnessing increased…

Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems…

Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we…

The main challenge with the tensor completion problem is a fundamental tension between computation power and the information-theoretic sample complexity rate. Past approaches either achieve the information-theoretic rate but lack practical…

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…

With the increasing adoption of machine learning tools like neural networks across several domains, interesting connections and comparisons to concepts from other domains are coming to light. In this work, we focus on the class of Tensor…

ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagram notation, which allows users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The…

Tensor Network methods have been established as a powerful technique for simulating low dimensional strongly-correlated systems for over two decades. Employing the formalism of Matrix Product States, we investigate the phase diagram of the…

It is challenging to reduce the complexity of neural networks while maintaining their generalization ability and robustness, especially for practical applications. Conventional solutions for this problem incorporate quantum-inspired neural…

Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…

A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central…

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or…

An effective neural network algorithm of the perceptron type is proposed. The algorithm allows us to identify strongly distorted input vector reliably. It is shown that its reliability and processing speed are orders of magnitude higher…

Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…

This paper studies the prediction task of tensor-on-tensor regression in which both covariates and responses are multi-dimensional arrays (a.k.a., tensors) across time with arbitrary tensor order and data dimension. Existing methods either…

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…