Related papers: The Tensor Network Theory Library

SOL is an open-source library for scalable online learning algorithms, and is particularly suitable for learning with high-dimensional data. The library provides a family of regular and sparse online learning algorithms for large-scale…

A method for online tensor dictionary learning is proposed. With the assumption of separable dictionaries, tensor contraction is used to diminish a $N$-way model of $\mathcal{O}\left(L^N\right)$ into a simple matrix equation of…

On the lattice, a renormalization group (RG) flow for two-dimensional partition functions expressed as a tensor network can be obtained using the tensor network renormalization (TNR) algorithm [G. Evenbly, G. Vidal, Phys. Rev. Lett. 115…

Simulation is essential for developing quantum hardware and algorithms. However, simulating quantum circuits on classical hardware is challenging due to the exponential scaling of quantum state space. While factorized tensors can greatly…

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…

Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…

We propose a new tensor network renormalization group (TNR) scheme based on global optimization and introduce a new method for constructing the finite-temperature density matrix of two-dimensional quantum systems. Combining these two into a…

Active inference provides a general framework for behavior and learning in autonomous agents. It states that an agent will attempt to minimize its variational free energy, defined in terms of beliefs over observations, internal states and…

Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of…

Modern transportation network modeling increasingly involves the integration of diverse methodologies including sensor-based forecasting, reinforcement learning, classical flow optimization, and demand modeling that have traditionally been…

Quantum machine learning researchers often rely on incorporating Tensor Networks (TN) into Deep Neural Networks (DNN) and variational optimization. However, the standard optimization techniques used for training the contracted trainable…

We introduce SeeMPS, a Python library dedicated to implementing tensor network algorithms based on the well-known Matrix Product States (MPS) and Quantized Tensor Train (QTT) formalisms. SeeMPS is implemented as a complete finite precision…

Uncertainty estimation is crucial in scientific data for machine learning. Current uncertainty estimation methods mainly focus on the model's inherent uncertainty, while neglecting the explicit modeling of noise in the data. Furthermore,…

While current time series research focuses on developing new models, crucial questions of selecting an optimal approach for training such models are underexplored. Tsururu, a Python library introduced in this paper, bridges SoTA research…

We introduce NetKet, a comprehensive open source framework for the study of many-body quantum systems using machine learning techniques. The framework is built around a general and flexible implementation of neural-network quantum states,…

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…

The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…

We initiate an open-source library for the efficient analysis of temporal graphs. We consider one of the standard models of dynamic networks in which each edge has a discrete timestamp and transition time. Recently there has been a massive…

In recent years, spatio-temporal graph neural networks (GNNs) have attracted considerable interest in the field of time series analysis, due to their ability to capture, at once, dependencies among variables and across time points. The…

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…