On Spectral Learning for Odeco Tensors: Perturbation, Initialization, and Algorithms

Fuente: arXiv
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Autori principali: Auddy, Arnab, Yuan, Ming
Natura: Preprint
Pubblicazione: 2025
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author Auddy, Arnab
Yuan, Ming
author_facet Auddy, Arnab
Yuan, Ming
contents We study spectral learning for orthogonally decomposable (odeco) tensors, emphasizing the interplay between statistical limits, optimization geometry, and initialization. Unlike matrices, recovery for odeco tensors does not hinge on eigengaps, yielding improved robustness under noise. While iterative methods such as tensor power iterations can be statistically efficient, initialization emerges as the main computational bottleneck. We investigate perturbation bounds, non-convex optimization analysis, and initialization strategies, clarifying when efficient algorithms attain statistical limits and when fundamental barriers remain.
format Preprint
id arxiv_https___arxiv_org_abs_2509_25126
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On Spectral Learning for Odeco Tensors: Perturbation, Initialization, and Algorithms
Auddy, Arnab
Yuan, Ming
Machine Learning
Numerical Analysis
Statistics Theory
We study spectral learning for orthogonally decomposable (odeco) tensors, emphasizing the interplay between statistical limits, optimization geometry, and initialization. Unlike matrices, recovery for odeco tensors does not hinge on eigengaps, yielding improved robustness under noise. While iterative methods such as tensor power iterations can be statistically efficient, initialization emerges as the main computational bottleneck. We investigate perturbation bounds, non-convex optimization analysis, and initialization strategies, clarifying when efficient algorithms attain statistical limits and when fundamental barriers remain.
title On Spectral Learning for Odeco Tensors: Perturbation, Initialization, and Algorithms
topic Machine Learning
Numerical Analysis
Statistics Theory
url https://arxiv.org/abs/2509.25126