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.
Distance matrices and isometric embeddings
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abstract
We review the relations between distance matrices and isometric embeddings and give simple proofs that distance matrices defined on euclidean and spherical spaces have all eigenvalues except one non-negative. Several generalizations are discussed.
fields
cs.LG 2years
2026 2verdicts
UNVERDICTED 2representative 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.
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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.