Defines temporal matrix scale invariance (tMSI) for correlation kernels, decouples dynamical exponent α from spectral exponent β via Mellin factorization, and classifies tipping points by the sign of an exact Landau quartic coefficient a4 derived from those exponents and a three-point structure cons
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Introduces symmetry-aware convex shrinkage for high-dimensional covariance estimation by selecting a symmetry group via held-out negative log-likelihood and proving regret bounds plus dominance over Ledoit-Wolf under a match condition.
A PC-based decomposition of FVE into low- and high-dimensional components reduces bias when applying GWASH or LMM-REML to strongly correlated high-dimensional predictors.
Using random matrix theory, the authors prove spectral separability of mean-shift spikes and asymptotic invariance of the original eigenspace, then introduce a knockoff-mean two-stage PCA procedure to remove the contamination.
Resolvents of the sample covariances in the separable mixture model approximate deterministic matrices defined via solutions to a dual system of equations, without simultaneous diagonalizability assumptions.
Spectral condensation of eigen-microstate occupations, quantified by emergent-sector entropy, diagnoses finite nonequilibrium transitions such as polar-vortex breakdown in ERA5 data and a wave-mean-flow model.
Marchenko-Pastur random-matrix pruning of DNNs yields theoretical certificates for accuracy preservation under small fine-tuning and empirical ImageNet results with 50-60% MAC reduction and sub-2pp accuracy drops on ViT and CNN models.
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Spectral approximation for the separable covariance mixture model
Resolvents of the sample covariances in the separable mixture model approximate deterministic matrices defined via solutions to a dual system of equations, without simultaneous diagonalizability assumptions.