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

• URL: http://arxiv.org/abs/2509.25126v1
• Date: Mon, 29 Sep 2025 17:45:35 GMT
• Title: On Spectral Learning for Odeco Tensors: Perturbation, Initialization, and Algorithms
• Authors: Arnab Auddy, Ming Yuan,
• Abstract summary: We spectral learning for decomposable (odeco) tensors.<n>We focus on the interplay between statistical limits, geometry, and robustness.
• Score: 4.04411589138781
• License: http://creativecommons.org/licenses/by/4.0/
• 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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