Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.
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The space of rank-r core covariances forms a smooth manifold except on a measure-zero set, enabling a partial-isotropy shrinkage estimator for matrix-variate data.
A combinatorial formula is given for the Euler characteristic of the Grassmannian with d hyperplane sections removed, with focus on generic cases, Schubert divisors, and both complex and real settings.
Studies determinantal varieties and ideals of relations for symmetric matrices with zero diagonal blocks arising as Gram matrices in conformal field theory.
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Covariance Estimation for Matrix-variate Data via Fixed-rank Core Covariance Geometry
The space of rank-r core covariances forms a smooth manifold except on a measure-zero set, enabling a partial-isotropy shrinkage estimator for matrix-variate data.