因为这个图示像是一列火车,所以这种分解称为 Tensor Train Decomposition 或者简称 TT-分解。其中秩 rk 称为 压缩秩 或者TT-ranks。 2. 推导 假设有大小为 n1×n2×⋯×nd 的d 维张量 A,当存在大小为 rk−1×nk×rk,k=1,⋯,d,r0=rd=1 的三维张量 Gk且 这些核张量通过 Figure1-2 的公式可以计...
这篇文章主要是把全连接层的权重进行tensor-traindecomposition,且听我慢慢道来。 首先看最基础的全连接层: 那么,下一步,我们就是对W进行tensor-traindecomposition(忘记具体形式的可看我上篇文章)转换成张量形式,同样的,为了匹配W,我们把y,x,b也都
"Proximal Alternating Linearized Minimization Algorithm for Sparse Tensor Train Decomposition" (Hu & Chen, 2025, Statistics, Optimization & Information Computing) Experiments in the Paper and Corresponding Code Section 5.1: Synthetic Data Experiment CaseMATLAB Code Path Different μ Synthetic_data/Untitled1...
Oseledets写的Tensor-Train Decomposition论文写的挺全的，他还写过一系列的关于Tensor train的论文。tens...
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 versatile functionality for the Riemannian optimization framework, which ...
原文地址:http://www.xiongfuli.com/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/2016-06/tensor-decomposition-tucker.html Tucker分解 Tucker的1966年文章中第一次提到了Tucker分解。一个三阶张量的Tucker分解的图示如下图所示。 对于一个三阶张量, 由Tucker分解可以得到,,三个因... ...
Oseledets, Ivan V. "Tensor-train decomposition." SIAM Journal on Scientific Computing 33.5 (2011): 2295-2317.(Paper)(Matlab code)(Tensorflow code) To be continued Releases No releases published Packages No packages published Languages MATLAB99.3% ...
Cichocki, "Big data singular value decom- position based on low-rank tensor train decomposition," RIKEN BSI, Tech. Rep., 2014 (submitted).N. Lee and A. Cichocki. Big data matrix singular value decomposition based on low-rank tensor train decomposition. In Advances in Neural Networks, pages ...
We utilized Tucker decomposition, TensorTrain decomposition, and CP decomposition in LS-STM and evaluated their performance on previous datasets. The results from both sets of data, as shown in Supplementary Fig. 2, demonstrate the superior and robust performance of LS-STM across different ...
There are about a dozen other libraries implementing Tensor Train decomposition. The main difference betweent3fand other libraries is thatt3fhas extensive support for Riemannian optimization and that it uses TensorFlow as backend and thus supports GPUs, automatic differentiation, and batch processing. For...