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Cet article se veut un survol des r\'eseaux de tenseurs et s'adresse aux d\'ebutants en la mati\`ere. Nous y mettons l'accent sur les outils n\'ecessaires \`a l'impl\'ementation concr\`ete d'algorithmes. Quatre op\'erations de base…
Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory…
Compared to sequential learning models, graph-based neural networks exhibit some excellent properties, such as ability capturing global information. In this paper, we investigate graph-based neural networks for text classification problem.…
This tutorial material on Convolutional Neural Networks (CNN) and its applications in digital media research is based on the concept of Symbolic Tensor Neural Networks. The set of STNN expressions is specified in Backus-Naur Form (BNF)…
We present an overview of the key ideas and skills necessary to begin implementing tensor network methods numerically, which is intended to facilitate the practical application of tensor network methods for researchers that are already…
Many real-world data, such as recommendation data and temporal graphs, can be represented as incomplete sparse tensors where most entries are unobserved. For such sparse tensors, identifying the top-k higher-order interactions that are most…
Recurrent neural networks (RNNs) can learn continuous vector representations of symbolic structures such as sequences and sentences; these representations often exhibit linear regularities (analogies). Such regularities motivate our…
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…
Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors.…
The understanding of complex quantum many-body systems has been vastly boosted by tensor network (TN) methods. Among others, excitation spectrum and long-range interacting systems can be studied using TNs, where one however confronts the…
Graph classification is a significant problem in many scientific domains. It addresses tasks such as the classification of proteins and chemical compounds into categories according to their functions, or chemical and structural properties.…
Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using…
DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of…
The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…
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…
Let $T$ be a set, of {\em types}, and let $\iota,o:T\to\oZ_+$. A {\em $T$-diagram} is a locally ordered directed graph $G$ equipped with a function $\tau:V(G)\to T$ such that each vertex $v$ of $G$ has indegree $\iota(\tau(v))$ and…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
Deep neural networks (DNNs) have achieved outstanding performance in a wide range of applications, e.g., image classification, natural language processing, etc. Despite the good performance, the huge number of parameters in DNNs brings…
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…