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Math researchers prove sharp phase transition in random ellipsoid fitting

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Researchers have proven a conjecture regarding the phase transition in random ellipsoid fitting. The study demonstrates that as the dimensions and number of data points increase, a sharp transition occurs at approximately n ~ d^2/4. Below this threshold, an ellipsoid fit is likely to exist, even with specific spectral constraints, while above it, no fit is probable, regardless of spectral restrictions. The proof utilizes the Gaussian-equivalence framework and introduces new techniques for exact fitting and constraint removal. AI

RANK_REASON Academic paper detailing a mathematical proof and conjecture. [lever_c_demoted from research: ic=1 ai=0.1]

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Math researchers prove sharp phase transition in random ellipsoid fitting

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Academic paper detailing a mathematical proof and conjecture. [lever_c_demoted from research: ic=1 ai=0.1]
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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Theodor Misiakiewicz, Garrett G. Wen ·

    The sharp SAT/UNSAT phase transition in random ellipsoid fitting

    arXiv:2608.10184v1 Announce Type: cross Abstract: Let $x_1,\ldots,x_n$ be independent standard Gaussian vectors in $\mathbb{R}^d$. An \emph{ellipsoid fit} is a matrix $S \succeq 0$ such that $x_i^\top S x_i =d$ for every $i$, so that all the points lie on the boundary of the cent…

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