Related papers: The Augmented Tree Tensor Network Cookbook

With the development of technology, the chemical production process is becoming increasingly complex and large-scale, making fault detection particularly important. However, current detective methods struggle to address the complexities of…

The era of exascale computing opens new venues for innovations and discoveries in many scientific, engineering, and commercial fields. However, with the exaflops also come the extra-large high-dimensional data generated by high-performance…

The hierarchical equations of motion (HEOM) method is a numerically exact open quantum system dynamics approach. The method is rooted in an exponential expansion of the bath correlation function, which in essence strategically reshapes a…

It is widely recognized that the deeper networks or networks with more feature maps have better performance. Existing studies mainly focus on extending the network depth and increasing the feature maps of networks. At the same time,…

Multi-Task Learning (MTL) has shown its importance at user products for fast training, data efficiency, reduced overfitting etc. MTL achieves it by sharing the network parameters and training a network for multiple tasks simultaneously.…

We determine the computational power of isometric tensor network states (isoTNS), a variational ansatz originally developed to numerically find and compute properties of gapped ground states and topological states in two dimensions. By…

This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics…

We present a new variational tree tensor network state (TTNS) ansatz, the three-legged tree tensor network state (T3NS). Physical tensors are interspersed with branching tensors. Physical tensors have one physical index and at most two…

The recently introduced locally orderless tensor network (LoTeNet) for supervised image classification uses matrix product state (MPS) operations on grids of transformed image patches. The resulting patch representations are combined back…

The complexity and scale of IT systems are increasing dramatically, posing many challenges to real-world anomaly detection. Deep learning anomaly detection has emerged, aiming at feature learning and anomaly scoring, which has gained…

We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

Deep neural networks (DNNs) can be useful within the marine robotics field, but their utility value is restricted by their black-box nature. Explainable artificial intelligence methods attempt to understand how such black-boxes make their…

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

Tensor network methods are powerful and efficient tools to study the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods were applied to lattice gauge theories,…

Network structures and models have been widely adopted, e.g., for Internet of Things, wireless sensor networks, smart grids, transportation networks, communication networks, social networks, and computer grid systems. Network reliability is…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

On the one hand, artificial neural networks (ANNs) are commonly labelled as black-boxes, lacking interpretability; an issue that hinders human understanding of ANNs' behaviors. A need exists to generate a meaningful sequential logic of the…

We present a general computational framework to investigate ground state properties of quantum spin models on infinite two-dimensional lattices using automatic differentiation-based gradient optimization of infinite projected entangled-pair…

We consider a model of strongly correlated electrons in 1D called the t-J model, which was solved by graded algebraic Bethe ansatz. We use it to design graded tensor networks which can be contracted approximately to obtain a Matrix Product…