SSA and DA extract barrier-sensitive mode separation from the autocovariance matrix of a unique constant-coefficient diffusion with the given density as stationary distribution.
The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices.Advances in Mathematics, 227(1):494–521
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In an anisotropic random-matrix model of gradient flow, the teacher signal produces a transient BBP transition where the outlier eigenvalue emerges only in an intermediate time window before overfitting.
The KL generalization error in unsupervised learning decomposes exactly into model error, data bias, and variance for e-flat models, with closed-form results for ε-PCA on isotropic Gaussians showing optimal rank at the noise floor and a three-regime phase diagram.
Finite-rank normal perturbations of large rotationally invariant non-Hermitian random matrices produce outlier eigenvalues whose positions and fluctuations, together with the associated eigenvectors, are characterized in a unified framework that includes the Hermitian case.
An algorithm reduces finding parameter conditions for specific eigenvalue configurations of two parametric symmetric matrices to real root counting of symmetric polynomials via the Fundamental Theorem of Symmetric Polynomials and Descartes' rule of signs.
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SSA and DA extract barrier-sensitive mode separation from the autocovariance matrix of a unique constant-coefficient diffusion with the given density as stationary distribution.
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In an anisotropic random-matrix model of gradient flow, the teacher signal produces a transient BBP transition where the outlier eigenvalue emerges only in an intermediate time window before overfitting.
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Information-Geometric Decomposition of Generalization Error in Unsupervised Learning
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The eigenvalues and eigenvectors of finite-rank normal perturbations of large rotationally invariant non-Hermitian matrices
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An algorithm reduces finding parameter conditions for specific eigenvalue configurations of two parametric symmetric matrices to real root counting of symmetric polynomials via the Fundamental Theorem of Symmetric Polynomials and Descartes' rule of signs.