Jul 2026· Numerical Linear Algebra with Applications· Vol 33· 0 citations· 18 references
Abstract
In this work, we present the tree tensor network Nyström (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, enabling a unified treatment of various existing methods. Our method retains the key features of the generalized Nyström approximation for matrices, that is, randomized, single‐pass, streamable, and cost‐effective. Additionally, the structure of the sketches allows for parallel implementation. We provide a deterministic error bound for the algorithm and, in the specific case of Gaussian dimension reduction maps, also a probabilistic one. We also introduce a sequential variant of the algorithm, referred to as sequential tree tensor network Nyström (STTNN), which offers better performance for dense tensors. Furthermore, both algorithms are well‐suited for the recompression or rounding of tensors in the tree tensor network format. Numerical experiments highlight the efficiency and effectiveness of the proposed methods.
This work presents the tree tensor network Nyström (TTNN), an algorithm that extends recent research on streamable tensor approximation to the more general tree tensor network format, enabling a unified treatment of various existing methods.
Alberto Bucci, Gianfranco Verzella· Numerical Linear Algebra wit...· 3 citations
A novel reformulation of the butterfly structure as a compact tensor network is proposed, leading to speedups of orders of magnitude and significant accuracy improvements for large matrices compared to state‐of‐the‐art low‐rank matrix and QTT tensor completion algorithms.
Navjot Singh, Edgar Solomonik, X. Li et al.· Numerical Linear Algebra wit...· 0 citations
A new SVD-based tensor decomposition method for tensor networks with arbitrary graph topologies is introduced, and it is found that the graph-format representation attains comparable or better accuracy than the classical tensor train and hierarchical Tucker tensor formats, while using substantially fewer degrees of fre...
Tensor networks are powerful formats for compressing large-scale data. However, their application to general data processing has been limited by the difficulty of performing nonlinear operations. Here, we introduce iterative tensor network transformations (ITNTs), a general algorithmic framework for the element-wise ev...
Xiao Wang, Tomohiro Hashizume, Pia Siegl et al.· 2 citations
An efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format and observing that the proposed NTT fitting procedure exhibits drastically faster convergence than an alternative multiplicative update method that has been previously proposed...
Xun Tang, Rajat Vadiraj Dwaraknath, Le-Xing Ying· SIAM Journal on Scientific C...· 0 citations
Traditional model reduction techniques for neural network compression usually leverage existing matrix/tensor decomposition methods to explore the redundancy among model parameters, which may overlook the local structures of the models. In this work, we propose a novel low-rank approximation algorithm, called Dimension...
Yu-Chuan Tai, Cheng-Yu Sie, Che-Rung Lee· Annual International Compute...· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
