Related papers: Efficient Tensor Network Algorithms for Spin Foam …

Recurrent neural networks have proved to be an effective method for statistical language modeling. However, in practice their memory and run-time complexity are usually too large to be implemented in real-time offline mobile applications.…

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…

Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…

Tensor-network Born machines (TNBMs) are quantum-inspired generative models for learning data distributions. Using tensor-network contraction and optimization techniques, the model learns an efficient representation of the target…

General matrix-matrix multiplication (GEMM) is a cornerstone of AI computations, making tensor processing engines (TPEs) increasingly critical in GPUs and domain-specific architectures. Existing architectures primarily optimize dataflow or…

One of the most pressing issues for loop quantum gravity and spin foams is the construction of the continuum limit. In this paper, we propose a systematic coarse-graining scheme for three-dimensional lattice gauge models including spin…

We propose a scalable tensorization framework for neural network compression based on slice-wise feature distillation. Unlike conventional tensor decomposition methods that rely on costly global finetuning, our approach decomposes the…

We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…

Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…

Second-order federated learning (FL) algorithms offer faster convergence than their first-order counterparts by leveraging curvature information. However, they are hindered by high computational and storage costs, particularly for…

We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment…

Participation factors (PFs) quantify the interaction between system modes and state variables, and they play a crucial role in various applications such as modal analysis, model reduction, and control design. With increasing system…

In this thesis we extend the formalism of tensor network algorithms to incorporate global internal symmetries. We describe how to both numerically protect the symmetry and exploit it for computational gain in tensor network simulations. Our…

We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low…

Modern sensing and metrology systems now stream terabytes of heterogeneous, high-dimensional (HD) data profiles, images, and dense point clouds, whose natural representation is multi-way tensors. Understanding such data requires regression…

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…

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…

Tight and efficient neural network bounding is crucial to the scaling of neural network verification systems. Many efficient bounding algorithms have been presented recently, but they are often too loose to verify more challenging…

There is an increasing interest in scaling tensor network methods through belief propagation (BP), as well as increasing the accuracy of BP through tensor network methods. We develop a unification framework that takes an arbitrary graphical…

Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of…