Related papers: Efficient Tensor Network Algorithms for Spin Foam …
Accurately reconstructing a three-dimensional ocean sound speed field (3D SSF) is essential for various ocean acoustic applications, but the sparsity and uncertainty of sound speed samples across a vast ocean region make it a challenging…
Tensor networks have been an important concept and technique in many research areas, such as quantum computation and machine learning. We study the exponential complexity of contracting tensor networks on two special graph structures:…
We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…
Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. These methodologies have been adapted recently for solving the Navier-Stokes equations, which…
This work discusses tensor network embeddings, which are random matrices ($S$) with tensor network structure. These embeddings have been used to perform dimensionality reduction of tensor network structured inputs $x$ and accelerate…
Multi-scale, multi-fidelity numerical simulations form the pillar of scientific applications related to numerically modeling fluids. However, simulating the fluid behavior characterized by the non-linear Navier Stokes equations are often…
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
The deployment of convolutional neural networks is often hindered by high computational and storage requirements. Structured model pruning is a promising approach to alleviate these requirements. Using the VGG-16 model as an example, we…
To respond to the need of efficient training and inference of deep neural networks, a plethora of domain-specific hardware architectures have been introduced, such as Google Tensor Processing Units and NVIDIA Tensor Cores. A common feature…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
Implicit neural representations have recently been extended to represent convolutional neural network weights via neural representation for neural networks, offering promising parameter compression benefits. However, standard multi-layer…
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…
The rapid growth in complexity and size of modern deep neural networks (DNNs) has increased challenges related to computational costs and memory usage, spurring a growing interest in efficient model compression techniques. Previous…
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 an algorithm that aims at minimizing the inter-node communication volume for distributed and memory-efficient tensor contraction schemes on modern multi-core compute nodes. The key idea is to define processor grids that optimize…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
This paper is a manual with tips and tricks for programming tensor network algorithms with global $SU(2)$ symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of…
From the moment Neural Networks dominated the scene for image processing, the computational complexity needed to solve the targeted tasks skyrocketed: against such an unsustainable trend, many strategies have been developed, ambitiously…
We provide an algorithm to estimate the divergence degree of the Lorentzian EPRL-FK spin foam amplitudes for arbitrary 2-complexes. We focus on the "self-energy" and "vertex renormalization" diagrams and find an upper bound estimate. We…
Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…