A majorization relation for a sum of two tensor products of positive semidefinite operators
arXiv:2607.07913
2026
Regularization
1 ideas extracted · analyzed Aug 30, 2026
What the math gives to ML
The paper proves a nontrivial spectral inequality for a sum of two Kronecker products of positive semidefinite matrices: the full eigenvalue vector is majorized by the componentwise sum of the Kronecker products of the factor eigenvalue vectors. This gives computable upper bounds on every Ky Fan spectral sum of a huge tensorized PSD operator using only eigendecompositions of its small factors. A practical transfer is a spectral regularizer or adaptive stability controller for Kronecker-factorized layers, covariance operators, Fisher approximations, or attention kernels represented as two separable PSD terms.
Ideas from this paper
Unverified
2026
Represent a large positive semidefinite neural operator as the sum of two Kronecker products and regularize an efficiently computed upper bound on its largest eigenvalues. The bound controls not only the spectral norm but every top-k eigenvalue sum, allowing a tunable penalty on concentrated or unstable directions without constructing the exponentially larger operator.
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