Observable Matrix Dynamics (OMD) is a new diagnostic framework that uses random matrix theory on distance matrices to distinguish diffusive relaxations from phase-transition-like reorganizations during neural network training.
Spectral properties of distance matrices
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abstract
Distance matrices are matrices whose elements are the relative distances between points located on a certain manifold. In all cases considered here all their eigenvalues except one are non-positive. When the points are uncorrelated and randomly distributed we investigate the average density of their eigenvalues and the structure of their eigenfunctions. The spectrum exhibits delocalized and strongly localized states which possess different power-law average behaviour. The exponents depend only on the dimensionality of the manifold.
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UNVERDICTED 3representative citing papers
I-BBS recovers latent manifold dimension d and geometry from ambient distance matrices via two noise-stable integer signatures: top non-Perron multiplet multiplicity and a parameter-free shrinkage law.
Dynamic distance matrices from Brownian particles on a sphere preserve the static BBS spectral template, with mass redistribution providing diagnostics for ring formation in the underlying point process.
citing papers explorer
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Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions
Observable Matrix Dynamics (OMD) is a new diagnostic framework that uses random matrix theory on distance matrices to distinguish diffusive relaxations from phase-transition-like reorganizations during neural network training.
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I-BBS: Coordinate-Free Inference of Latent Sub-Manifolds Using Random Distance Matrix Theory
I-BBS recovers latent manifold dimension d and geometry from ambient distance matrices via two noise-stable integer signatures: top non-Perron multiplet multiplicity and a parameter-free shrinkage law.
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Frustrated Dynamics of Distance Matrices
Dynamic distance matrices from Brownian particles on a sphere preserve the static BBS spectral template, with mass redistribution providing diagnostics for ring formation in the underlying point process.