Related papers: The Tensor Network Theory Library

Tensor network machine learning models have shown remarkable versatility in tackling complex data-driven tasks, ranging from quantum many-body problems to classical pattern recognitions. Despite their promising performance, a comprehensive…

The string-net condensate is a new class of materials which exhibits the quantum topological order. In order to answer the important question, "how useful is the string-net condensate in quantum information processing?", we consider the…

Tensor networks are a very powerful data structure tool originating from quantum system simulations. In recent years, they have seen increased use in machine learning, mostly in trainings with gradient-based techniques, due to their…

HOTTBOX is a Python library for exploratory analysis and visualisation of multi-dimensional arrays of data, also known as tensors. The library includes methods ranging from standard multi-way operations and data manipulation through to…

Logic Tensor Networks (LTN) is a Neuro-Symbolic framework that effectively incorporates deep learning and logical reasoning. In particular, LTN allows defining a logical knowledge base and using it as the objective of a neural model. This…

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…

Atomic neural networks (ANNs) constitute a class of machine learning methods for predicting potential energy surfaces and physico-chemical properties of molecules and materials. Despite many successes, developing interpretable ANN…

We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in…

In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of…

Over the last two decades, alongside the increased availability of large network datasets, we have witnessed the rapid rise of network science. For many systems, however, the data we have access to is not a direct description of the…

The computation and storage requirements for Deep Neural Networks (DNNs) are usually high. This issue limits their deployability on ubiquitous computing devices such as smart phones, wearables and autonomous drones. In this paper, we…

Tensor networks (TNs) provide efficient representations of high-dimensional data, yet identification of the optimal TN structures, the so called tensor network structure search (TN-SS) problem, remains a challenge. Current state-of-the-art…

Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…

Network theory provides tools which are particularly appropriate for assessing the complex interdependencies that characterise our modern connected world. This article presents an introduction to network theory, in a way that doesn't…

Number Theoretic Transform (NTT) is an essential mathematical tool for computing polynomial multiplication in promising lattice-based cryptography. However, costly division operations and complex data dependencies make efficient and…

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,…

This book is intended for teaching Signal Analysis methods and Inverse Problems theory. It is completely open access and will remain free. It is currently illustrated with examples that we have actually encountered in geophysics, but will…

We are upgrading the Python-version of RTNI, which symbolically integrates tensor networks over the Haar-distributed unitary matrices. Now, PyRTNI2 can treat the Haar-distributed orthogonal matrices and the real and complex normal Gaussian…

Tensor networks are factorisations of high rank tensors into networks of lower rank tensors and have primarily been used to analyse quantum many-body problems. Tensor networks have seen a recent surge of interest in relation to supervised…

Neural machine translation (NMT) heavily relies on word-level modelling to learn semantic representations of input sentences. However, for languages without natural word delimiters (e.g., Chinese) where input sentences have to be tokenized…