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New bounds for random fields applied to Tensor PCA and spin models

By PulseAugur Editorial · [2 sources] ·

Researchers have developed new non-asymptotic tail bounds for the Kostlan--Shub--Smale (KSS) random field on the sphere. These bounds are applied to problems in Spiked Tensor PCA and the complexity of the spherical $k$-spin model. The work establishes explicit constants for error bounds in estimation and complexity functions in high-dimensional limits. AI

IMPACT Advances theoretical understanding of random fields, potentially impacting future AI model development and analysis.

RANK_REASON The cluster contains an academic paper published on arXiv detailing theoretical advancements in statistics and machine learning.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New bounds for random fields applied to Tensor PCA and spin models

COVERAGE [2]

  1. arXiv stat.ML TIER_1 English(EN) · Jean-Marc Aza\"is (IMT), Federico Dalmao (UDELAR), Yohann De Castro (ICJ, ECL, PSPM, IUF) ·

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

    arXiv:2606.17665v1 Announce Type: cross Abstract: This paper builds a hierarchy of explicit, non-asymptotic tail bounds for the supremum of the Kostlan--Shub--Smale (KSS) random field on the sphere, and applies it to two problems: Spiked Tensor PCA and the landscape of the spheri…

  2. arXiv stat.ML TIER_1 English(EN) · Yohann De Castro ·

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

    This paper builds a hierarchy of explicit, non-asymptotic tail bounds for the supremum of the Kostlan--Shub--Smale (KSS) random field on the sphere, and applies it to two problems: Spiked Tensor PCA and the landscape of the spherical $k$-spin model. For Tensor PCA, we study the n…

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