Universality of General Spiked Tensor Models

• URL: http://arxiv.org/abs/2602.04472v1
• Date: Wed, 04 Feb 2026 11:59:30 GMT
• Title: Universality of General Spiked Tensor Models
• Authors: Yanjin Xiang, Zhihua Zhang,
• Abstract summary: We study the rank-one spiked tensor model in the high-dimensional regime.<n>We show that their high-dimensional spectral behavior and statistical limits are robust to non-Gaussian noise.
• Score: 9.454986540713655
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We study the rank-one spiked tensor model in the high-dimensional regime, where the noise entries are independent and identically distributed with zero mean, unit variance, and finite fourth moment.This setting extends the classical Gaussian framework to a substantially broader class of noise distributions.Focusing on asymmetric tensors of order $d$ ($\ge 3$), we analyze the maximum likelihood estimator of the best rank-one approximation.Under a mild assumption isolating informative critical points of the associated optimization landscape, we show that the empirical spectral distribution of a suitably defined block-wise tensor contraction converges almost surely to a deterministic limit that coincides with the Gaussian case.As a consequence, the asymptotic singular value and the alignments between the estimated and true spike directions admit explicit characterizations identical to those obtained under Gaussian noise. These results establish a universality principle for spiked tensor models, demonstrating that their high-dimensional spectral behavior and statistical limits are robust to non-Gaussian noise. Our analysis relies on resolvent methods from random matrix theory, cumulant expansions valid under finite moment assumptions, and variance bounds based on Efron-Stein-type arguments. A key challenge in the proof is how to handle the statistical dependence between the signal term and the noise term.

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