The Subgroup Algorithm for Generating Uniform Random Variables

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Early Stopping without a Validation Set (2017, background): “In this controlled environment we can test the EB-criterion on different configurations of eigen-spectra, for example uniform, exponential, or structured (a few large, many small eigenvalues); the matrix B is constructed by defining a diagonal matrix Γ ∈ RD×D which contains the eigenvalues on its di”
How to generate random matrices from the classical compact groups (2006, unknown): “ar X iv :m at h- ph /0 60 90 50 v2 2 7 Fe b 20 07”
The Theory of Quantum Information (2018, background): “These definitions are rooted in the work of Dyson [64, 65, 66] and Diaconis and Shahshahani [60], and a more broad overview of random matrix theory may be found in the book of Mehta [156].”
Follow the Signs for Robust Stochastic Optimization (2017, methodology): “To control eigenspectrum and -basis, we specify a diagonal matrix Λ of eigenvalues and generate a Hessian H by (a) drawing a rotation matrix R at random [5], and choosing H = RΛR , or (b) simply setting H = Λ.”
Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients (2017, unknown): “Q is then deﬁned as (a) Q = Λ for an axis-aligned problem and (b) Q = R Λ R T with a random R drawn uniformly among all rotation matrices (see Diaconis & Shahshahani, 1987).”