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About this paper
Frederic Koehler, Youngtak Sohn
The authors study whether random points can lie on one positive-semidefinite ellipsoid, with each point satisfying the same quadratic-form constraint. Under independent, mean-zero, variance-one coordinates with shared fourth moment κ and bounded subgaussian norm, they identify a sharp sample-load threshold. For Gaussian points it is d²/4: below it a well-conditioned fit exists; above it no fit exists with high probability.
Summary by alphaXiv.
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