Finite-Iteration Local Dynamics and Warm Starts for Alternating Power Iteration in Spiked Tensor PCA
arXiv:2606.04065v1 Announce Type: cross Abstract: We study simultaneous alternating power iteration for fixed-order asymmetric rank-one spiked tensor models. Our main contribution is a finite-iteration local theory that is independent of any particular initialization. Once the iterates enter a sufficiently small neighborhood of the planted rank-one direction, their error decomposes into a geometrically decaying transient and an intrinsic noise floor caused by fixed orthogonal noise contractions at the planted point. The deterministic finite-sample conditions are stated explicitly, but under a
This is a theoretical computer science paper, a routine publication in the field of AI and machine learning research.
It contributes to the foundational understanding of tensor decomposition algorithms, which are crucial for advanced machine learning models but is highly academic.
No immediate change; this is a mathematical refinement for a specific algorithm rather than a breakthrough in applied AI.
Refinement of mathematical understanding for alternating power iteration in spiked tensor PCA.
Potentially enables more robust or efficient tensor-based machine learning algorithms in the distant future.
Could contribute to the development of new theoretical guarantees for high-dimensional data analysis methods.
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