Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions
Observable Matrix Dynamics (OMD) is a diagnostic framework that probes the dynamics of high-dimensional internal representations of inputs by a neural network via a fixed-size $N \times N$ distance matrix $M(t)$ on a held set of $N$ inputs. OMD uses methods of random matrix theory and particle dynamics to explore spectral reorganisations that are missed by scalar loss functions, but are informative of the training process. We read $M(t)$ against a perturbative ambient-versus-latent decomposition extending the Bogomolny--Bohigas--Schmit (BBS) theory of random distance matrices, with per-snapshot diagnostics for the top-of-spectrum band structure and ambient noise, trajectory-level observab...
| Authors | Igor Halperin |
|---|---|
| Primary category | cs.LG |
| Published | 29 June 2026 |
| Last updated at source | 29 June 2026 |
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