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

2025/09/29 by Arnab Auddy, Ming Yuan, Auddy, Arnab +1
Engineering · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Statistics Theory (math.ST) #Tensor decomposition and applications #Vibration and Dynamic Analysis

paper · pdf · doi:10.48550/arxiv.2509.25126

openalex publication_date 2025/09/29 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

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.

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