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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,291 papers · 148 categories

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3 results for “Eckart-Young-Mirsky”

On the geometry of the set of symmetric matrices with repeated eigenvaluesmath.AG

Study geometric properties of symmetric matrices with repeated eigenvalues.

problem Investigate geometric properties of symmetric matrices with repeated eigenvalues.

method Explicitly compute the volume of the intersection with the sphere and prove an Eckart-Young-Mirsky-type theorem.

result Prove connections to Real Algebraic Geometry and Random Matrix Theory.

symmetric matrices eigenvalues geometric properties volume Eckart-Young-Mirsky

2018-07-12abs ↗pdf ↗

Rank/Norm Regularization with Closed-Form Solutions: Application to Subspace Clusteringcs.LG

When data is sampled from an unknown subspace, principal component analysis (PCA) provides an effective way to estimate the subspace and hence reduce the dimension of the data. At the heart of PCA is the Eckart-Young-Mirsky theorem, which characterizes the best rank k approximation of a matrix. In this paper, we prove …

2012-02-14abs ↗pdf ↗

Singular Bayesian Neural Networksstat.ML

Bayesian neural networks can be simplified by parameterizing weights as rank- $r$ matrices, reducing parameter count and improving performance.

problem High parameter count in standard Bayesian neural networks.

method Parameterize weights as

W = AB^{ op}

with

A \in \mathbb{R}^{m imes r}

B \in \mathbb{R}^{n imes r}

, inducing a singular posterior.

result PAC-Bayes generalization bounds and loss bounds show improved performance with fewer parameters.

Bayesian neural networks singular value decomposition parameter reduction generalization bounds low-rank approximation

2026-01-30abs ↗pdf ↗