On Spectral Learning for Odeco Tensors: Perturbation, Initialization, and Algorithms
This work addresses computational challenges in tensor decomposition for machine learning applications, but it appears incremental as it builds on existing iterative methods and analysis.
The paper tackles the problem of spectral learning for orthogonally decomposable tensors, showing that recovery does not depend on eigengaps, leading to improved robustness under noise, and identifies initialization as the main computational bottleneck.
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.