What question did this study set out to answer?

This research aims to establish explicit, non-asymptotic tail bounds for the supremum of the KSS random field and apply them to Tensor PCA and spherical k-spin models.

June 20, 2026Open Access

Non-asymptotic Tail Bounds for the Kostlan--Shub--Smale Field: Tensor PCA and Spherical k-Spin Complexity

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Authors

JAJean‐Marc AzäisUniversité Fédérale de Toulouse Midi-Pyrénées FDFederico DalmaoUniversidad de la República de Uruguay YCYohann de CastroInternational Council on Mining and Metals

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Randomized study investigates tail bounds for tensor PCA and spherical k-spin complexity, highlighting statistical limits.

Key Points

This research aims to establish explicit, non-asymptotic tail bounds for the supremum of the KSS random field and apply them to Tensor PCA and spherical k-spin models.
Develops a hierarchy of explicit tail bounds for the KSS random field on the sphere.
Applies the Tube Method to bound estimation error in Tensor PCA estimates for rank-R tensors.
Uses Gaussian integrals and the Kac–Rice formula to connect tail bounds to estimation accuracy.
Achieves a finite-(k,d) error bound that recovers asymptotically optimal rates with explicit dependence on rank R and coherence κ.
Establishes a non-asymptotic bracketing of the annealed complexity for the spherical k-spin Hamiltonian that aligns with established high-dimensional limit functions.

Cite This Study

Azäis et al. (2026) studied this question.

synapsesocial.com/papers/6a362de1db0793dc1a535dc6 https://doi.org/10.48550/arxiv.2606.17665

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Non-asymptotic Tail Bounds for the Kostlan--Shub--Smale Field: Tensor PCA and Spherical k-Spin Complexity

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Cite This Study

Non-asymptotic Tail Bounds for the Kostlan--Shub--Smale Field: Tensor PCA and Spherical k-Spin Complexity

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Key Points

Cite This Study

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