Non-Hermitian Random Matrix Theory of Jamming in Active Disordered Media

What the math gives to ML

The paper offers a transferable mechanism: a nearly reciprocal Wishart-like stiffness or Jacobian matrix acquires a non-Hermitian perturbation, and the resulting complex-spectrum and resolvent structure removes the soft-mode divergence found at a jamming transition. The neural-network analogue is to model layer Jacobians or recurrent state-transition matrices as a structured symmetric positive-semidefinite component plus a controlled non-reciprocal component, then monitor the smallest singular value and resolvent norm rather than eigenvalues alone. The useful prediction is a crossover at which the perturbation scale becomes comparable to the passive spectral gap: susceptibility should change from gap-dominated divergence to activity-dominated saturation. This can yield a non-normality-aware regularizer or stability controller for RNNs, state-space models, and optimizer dynamics.