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A Geometric Phase Boundary for Volume-Sampled Linear Readouts

arXiv · AI, language, vision and robotics · article · Aug 27, 2026 · UTC

Global sharpness of a sampling bound does not determine whether the bound is attainable on a particular fixed design. We study ordinary fixed-size volume sampling followed by selected unweighted least squares, with the feature pool and response fixed; subset selection is the only randomness. We first prove a globally sharp all-budget Loewner envelope for centered, full-Gram-whitened coefficient covariance. We then characterize the fixed-design question left open by global sharpness. On the positive-loss, no-coloop strict-interior domain, a feature-only geometric margin is positive if and only

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