The paper introduces a new semi‑tensor product for third‑order tensors that relaxes the dimensional constraints of the standard t‑product while preserving the closed‑form nature of T‑SVD. It builds a multi‑term semi‑tensor product singular value decomposition (MSTP‑SVD) that improves low‑rank approximation accuracy, and further accelerates it with randomized projection and power iteration to create the MRSTP‑SVD algorithm. Experiments on image and video compression and completion show that this method balances reconstruction accuracy and computational efficiency.
By Xingchen Xiao (School of Mathematics and Statistics, Southwest University, Chongqing, China), Feng Zhang (School of Mathematics and Statistics, Southwest University, Chongqing, China), Wenjin Qin (School of Mathematics and Statistics, Southwest University, Chongqing, China), Jianjun Wang (School of Mathematics and Statistics, Southwest University, Chongqing, China)
arXiv:2606. 25975v1 Announce Type: new Abstract: Common first-order optimizers, such as Adam, implicitly treat each parameter block as an unstructured vector, which disregards the multilinear weight structure present in many modern machine learning models.
By Vladimir Bogachev, Vladimir Aletov, Alexander Molozhavenko, Sergei Kudriashov, Maxim Rakhuba
Common first-order optimizers, such as Adam, implicitly treat each parameter block as an unstructured vector, which disregards the multilinear weight structure present in many modern machine learning models. Recent work has shown that exploiting matrix structure can improve optimization dynamics.
This survey reviews tensor methods applied to large language models, framing them through a seven‑stage lifecycle (tokenization, embeddings, pre‑training, adaptation, compression, inference, interpretability) and a component view (embeddings, attention, feed‑forward networks). It offers unified notation, theoretical foundations, and comparative analyses of tensorization strategies for Transformer components, while highlighting evaluation protocol differences and model scale effects. The paper also introduces a new metric, ρ_gap, to quantify the gap between theoretical memory savings and actual system‑level speedup, and connects tensor techniques to related efficiency and probabilistic methods.
By Matvei Tarasov, Salman Ahmadi-Asl, Andre L. F. de Almeida, Andrzej Cichocki
arXiv:2606. 03212v1 Announce Type: new Abstract: Low-rank tensor decomposition (TD) is usually effective on clean, fully observed data, but it often degrades under severe missingness or noise.
By Zerui Tao, Qibin Zhao
Large language models (LLMs) are built from structured high-dimensional objects such as token representations, weights, adaptation updates, caches, and activations, whose multilinear structure is unde...
arXiv:2608. 10351v1 Announce Type: new Abstract: In this work we present a method to accelerate the optimization of learning high dimensional functions using deep neural network (DNN).
By Karl Pierce, Yuehaw Khoo, Haizhao Yang
arXiv:2606. 31061v1 Announce Type: cross Abstract: Tensor Train (TT) decomposition is a powerful technique for analyzing high-dimensional data.
By Hiroki Takeda, Yuto Miyatake, Daisuke Furihata
arXiv:2606. 08565v1 Announce Type: cross Abstract: Tensor networks provide efficient representations for compressing large neural networks.
By Toshiaki Koike-Akino, Jing Liu, Ye Wang
arXiv:2608.23864v1 Announce Type: new
Abstract: Visual tokenizers increasingly inject semantic supervision into latent spaces to make downstream diffusion easier. Yet how these semantics should be or...
By Junqiu Yu, Pandeng Li, Yikai Wang, Jiaxing Zhao, Yujie Wei, Kaixun Jiang, Quanhao Li, Hongtao Yu, Zhihang Liu, Zhaohe Liao, Junjie Zhou, Yun Zheng, Yu Liu, Yanwei Fu
arXiv:2412. 07041v4 Announce Type: replace-cross Abstract: Recovering incomplete multidimensional tensor-structured data is a fundamental task in many real-world applications.
By Mengying Lei, Lijun Sun
arXiv:2608.23249v1 Announce Type: new
Abstract: We consider a multistatic radio-frequency imaging problem with anisotropy, in which the reflection from a point depends on the positions of the transmi...
By Amir Rezaei, Wen-Xin Pan, Giuseppe Caire