Critical Properties and Glass Transitions in Randomly Coupled Fields

What the math gives to ML

The paper identifies a nonstandard critical mechanism: in a large randomly coupled field system, critical behavior is controlled by the eigenvalue density near the spectral edge rather than by microscopic coupling details. For Wigner disorder, the correlation length diverges at criticality while susceptibility can remain finite, and the spherical model has a glass phase whose correlations remain pinned to their critical form. A direct neural-network transfer is to control the spectral edge of recurrent or deep-residual Jacobians, maintaining a prescribed distance from marginality to obtain long memory without unstable states or gradients. The mechanism yields a falsifiable transition in correlation time and gradient persistence when the effective edge crosses one.