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Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Machine Learning · Statistics 2017-08-03 Masaaki Imaizumi , Takanori Maehara , Kohei Hayashi

Tensor Train (TT) decompositions provide a powerful framework to compress grid-structured data, such as sampled function values, on regular Cartesian grids. Such high compression, in turn, enables efficient high-dimensional computations.…

Numerical Analysis · Mathematics 2026-01-08 Siddhartha E. Guzman , Egor Tiunov , Leandro Aolita

Tensor Train decomposition is used across many branches of machine learning. We present T3F -- a library for Tensor Train decomposition based on TensorFlow. T3F supports GPU execution, batch processing, automatic differentiation, and…

Mathematical Software · Computer Science 2020-03-04 Alexander Novikov , Pavel Izmailov , Valentin Khrulkov , Michael Figurnov , Ivan Oseledets

DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of…

Tensor decomposition is one of the fundamental technique for model compression of deep convolution neural networks owing to its ability to reveal the latent relations among complex structures. However, most existing methods compress the…

Computer Vision and Pattern Recognition · Computer Science 2021-12-08 Bo-Shiuan Chu , Che-Rung Lee

Although the convolutional neural networks (CNNs) have become popular for various image processing and computer vision task recently, it remains a challenging problem to reduce the storage cost of the parameters for resource-limited…

Machine Learning · Computer Science 2018-11-01 Chao Li , Zhun Sun , Jinshi Yu , Ming Hou , Qibin Zhao

Deep Convolutional Neural Networks (CNNs) are increasingly difficult to deploy on microcontrollers (MCUs) and lightweight NPUs (Neural Processing Units) due to their growing size and compute demands. Low-rank tensor decomposition, such as…

Computer Vision and Pattern Recognition · Computer Science 2025-11-18 Sudhakar Sah , Nikhil Chabbra , Matthieu Durnerin

The embedding layers transforming input words into real vectors are the key components of deep neural networks used in natural language processing. However, when the vocabulary is large, the corresponding weight matrices can be enormous,…

Computation and Language · Computer Science 2020-02-20 Oleksii Hrinchuk , Valentin Khrulkov , Leyla Mirvakhabova , Elena Orlova , Ivan Oseledets

Neuron pruning is an efficient method to compress the network into a slimmer one for reducing the computational cost and storage overhead. Most of state-of-the-art results are obtained in a layer-by-layer optimization mode. It discards the…

Computer Vision and Pattern Recognition · Computer Science 2018-12-18 Weijie Chen , Yuan Zhang , Di Xie , Shiliang Pu

Recurrent Neural Networks (RNNs) have been widely used in sequence analysis and modeling. However, when processing high-dimensional data, RNNs typically require very large model sizes, thereby bringing a series of deployment challenges.…

Computer Vision and Pattern Recognition · Computer Science 2021-04-21 Miao Yin , Siyu Liao , Xiao-Yang Liu , Xiaodong Wang , Bo Yuan

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…

Machine Learning · Computer Science 2021-06-24 Meraj Hashemizadeh , Michelle Liu , Jacob Miller , Guillaume Rabusseau

We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…

Numerical Analysis · Mathematics 2025-12-23 Martin Eigel , Charles Miranda , Anthony Nouy , David Sommer

We address the computational barrier of deploying advanced deep learning segmentation models in clinical settings by studying the efficacy of network compression through tensor decomposition. We propose a post-training Tucker factorization…

Image and Video Processing · Electrical Eng. & Systems 2024-04-19 Tobias Weber , Jakob Dexl , David Rügamer , Michael Ingrisch

Modern neural networks have revolutionized the fields of computer vision (CV) and Natural Language Processing (NLP). They are widely used for solving complex CV tasks and NLP tasks such as image classification, image generation, and machine…

Machine Learning · Computer Science 2023-07-25 Xingyi Liu , Keshab K. Parhi

Neural network (NN) designed for challenging machine learning tasks is in general a highly nonlinear mapping that contains massive variational parameters. High complexity of NN, if unbounded or unconstrained, might unpredictably cause…

Machine Learning · Computer Science 2025-05-23 Yong Qing , Ke Li , Peng-Fei Zhou , Shi-Ju Ran

The compression of deep neural networks (DNNs) to reduce inference cost becomes increasingly important to meet realistic deployment requirements of various applications. There have been a significant amount of work regarding network…

Machine Learning · Computer Science 2020-11-12 Tianyi Chen , Bo Ji , Yixin Shi , Tianyu Ding , Biyi Fang , Sheng Yi , Xiao Tu

In this paper, we propose an efficient numerical method to solve high-dimensional nonlinear filtering (NLF) problems. Specifically, we use the tensor train decomposition method to solve the forward Kolmogorov equation (FKE) arising from the…

Numerical Analysis · Mathematics 2019-08-13 Sijing Li , Zhongjian Wang , Stephen S. T. Yau , Zhiwen Zhang

The success of DNNs and their high computational requirements pushed for large codesign efforts aiming at DNN acceleration. Since DNNs can be represented as static computational graphs, static memory allocation and tiling are two crucial…

Hardware Architecture · Computer Science 2025-04-08 Victor J. B. Jung , Alessio Burrello , Francesco Conti , Luca Benini

We present TensoRF, a novel approach to model and reconstruct radiance fields. Unlike NeRF that purely uses MLPs, we model the radiance field of a scene as a 4D tensor, which represents a 3D voxel grid with per-voxel multi-channel features.…

Computer Vision and Pattern Recognition · Computer Science 2022-11-30 Anpei Chen , Zexiang Xu , Andreas Geiger , Jingyi Yu , Hao Su

In recent years, deep learning techniques have been introduced into the field of trajectory optimization to improve convergence and speed. Training such models requires large trajectory datasets. However, the convergence of low thrust (LT)…

Optimization and Control · Mathematics 2022-02-11 Ruida Xie , Andrew G. Dempster