Low-Rank Tensor Ring Model for Completing Missing Visual Data

Asif, M. Salman; Prater-Bennette, Ashley

doi:10.1109/icassp40776.2020.9053290

Cited by 8 publications

(2 citation statements)

References 21 publications

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“…Like other tensor decompositions, the ALS [17,23,2] is still considered the best algorithm for TC, especially when DMRG cannot be applied. Various variants of these two update schemes were proposed e.g., for the tensor completion problem [24,25,26,27,28,29,30,31,32], hyperspectral super-resolution [33]. For determination of bond dimensions,we refer to [34,35].…”

Section: Algorithms For Tc Decompositionmentioning

confidence: 99%

How to Train Unstable Looped Tensor Network

Phan¹,

Соболев²,

Ermilov³

et al. 2022

Preprint

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A rising problem in the compression of Deep Neural Networks is how to reduce the number of parameters in convolutional kernels and the complexity of these layers by low-rank tensor approximation. Canonical polyadic tensor decomposition (CPD) and Tucker tensor decomposition (TKD) are two solutions to this problem and provide promising results. However, CPD often fails due to degeneracy, making the networks unstable and hard to fine-tune. TKD does not provide much compression if the core tensor is big. This motivates using a hybrid model of CPD and TKD, a decomposition with multiple Tucker models with small core tensor, known as block term decomposition (BTD). This paper proposes a more compact model that further compresses the BTD by enforcing core tensors in BTD identical. We establish a link between the BTD with shared parameters and a looped chain tensor network (TC). Unfortunately, such strongly constrained tensor networks (with loop) encounter severe numerical instability, as proved by [1] and [2]. We study perturbation of chain tensor networks, provide interpretation of instability in TC, demonstrate the problem. We propose novel methods to gain the stability of the decomposition results, keep the network robust and attain better approximation. Experimental results will confirm the superiority of the proposed methods in compression of well-known CNNs, and TC decomposition under challenging scenarios.

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Section: Algorithms For Tc Decompositionmentioning

confidence: 99%

How to Train Unstable Looped Tensor Network

Phan¹,

Соболев²,

Ermilov³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Across a variety of applications, datasets are multimodal or multi-way and naturally modeled as high-order tensors (e.g., hyper-spectral imagery, video, network/graph relation arrays) [1][2][3][4][5][6][7][8]. At the same time, real-world data often contain sporadic highly deviating points (faulty entries) due to errors in data collection/storage or even adversarial data contamination.…”

Section: Introductionmentioning

confidence: 99%

Robust Barron-Loss Tucker Tensor Decomposition

Mozaffari¹,

Markopoulos²

2021

Preprint

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<p>In this work, we propose a new formulation for low-rank tensor approximation, with tunable outlier-robustness, and present a unified algorithmic solution framework. This formulation relies on a new generalized robust loss function (Barron loss), which encompasses several well-known loss-functions with variable outlier resistance. The robustness of the proposed framework is corroborated by the presented numerical studies on synthetic and real data.</p>

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Randomized algorithms for fast computation of low rank tensor ring model

Ahmadi‐Asl¹,

Cichocki²,

Phan³

et al. 2020

Mach. Learn.: Sci. Technol.

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This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tubal product (t-product). The random projection method is utilized to compute the important actions of the underlying data tensors and use them to get small sketches of the original data tensors, which are easier to handle. Due to the small size of the sketch tensors, deterministic approaches are applied to them to compute their GTSVDs. Then, from the GTSVD of the small sketch tensors, the GTSVD of the original large-scale data tensors is recovered. Some experiments are conducted to show the effectiveness of the proposed approaches.

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Low-Rank Tensor Ring Model for Completing Missing Visual Data

Cited by 8 publications

References 21 publications

How to Train Unstable Looped Tensor Network

How to Train Unstable Looped Tensor Network

Robust Barron-Loss Tucker Tensor Decomposition

Randomized algorithms for fast computation of low rank tensor ring model

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