Related papers: From Tree Tensor Network to Multiscale Entanglemen…

Large-scale Dynamic Networks (LDNs) are becoming increasingly important in the Internet age, yet the dynamic nature of these networks captures the evolution of the network structure and how edge weights change over time, posing unique…

Neural Tensor Networks (NTNs), which are structured to encode the degree of relationship among pairs of entities, are used in Logic Tensor Networks (LTNs) to facilitate Statistical Relational Learning (SRL) in first-order logic. In this…

We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…

Methods such as Layer Normalization (LN) and Batch Normalization (BN) have proven to be effective in improving the training of Recurrent Neural Networks (RNNs). However, existing methods normalize using only the instantaneous information at…

Exact many-body quantum problems are known to be computationally hard due to the exponential scaling of the numerical resources required. Since the advent of the Density Matrix Renormalization Group, it became clear that a successful…

TensorNetwork is an open source library for implementing tensor network algorithms in TensorFlow. We describe a tree tensor network (TTN) algorithm for approximating the ground state of either a periodic quantum spin chain (1D) or a lattice…

In this work, we present the tree tensor network Nystr\"om (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker and tensor-train formats, to the more general tree tensor network format,…

Neural networks have achieved state of the art results in many areas, supposedly due to parameter sharing, locality, and depth. Tensor networks (TNs) are linear algebraic representations of quantum many-body states based on their…

We review different descriptions of many--body quantum systems in terms of tensor product states. We introduce several families of such states in terms of known renormalization procedures, and show that they naturally arise in that context.…

Tree tensor networks (TTNs) provide a compact and structured representation of high-dimensional data, making them valuable in various areas of computational mathematics and physics. In this paper, we present a rigorous mathematical…

Large power systems are complex and real-time modeling of the grid for electromagnetic simulation (EMT) studies is impractical. In general, there are methods that reduce large power system into an equivalent network that requires less…

Recently, a class of tensor networks called isometric tensor network states (isoTNS) was proposed which generalizes the canonical form of matrix product states to tensor networks in higher dimensions. While this ansatz allows for efficient…

We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…

We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states (TNS). The ground-state wave function is represented as a linear superposition composed from a set of TNS…

Large, multi-dimensional clusters of entangled photons are among the most powerful resources for emerging quantum technologies, as they are predicted to enable global quantum networks or universal quantum computation. Here, we propose an…

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of…

Recurrent neural networks (RNNs) and transformers have been shown to be Turing-complete, but this result assumes infinite precision in their hidden representations, positional encodings for transformers, and unbounded computation time in…

Data in the form of images or higher-order tensors is ubiquitous in modern deep learning applications. Owing to their inherent high dimensionality, the need for subquadratic layers processing such data is even more pressing than for…

The fully-connected tensor network (FCTN) decomposition has gained prominence in the field of tensor completion owing to its powerful capacity to capture the low-rank characteristics of tensors. Nevertheless, the recovery of local details…

Quantization of weights of deep neural networks (DNN) has proven to be an effective solution for the purpose of implementing DNNs on edge devices such as mobiles, ASICs and FPGAs, because they have no sufficient resources to support…