Correlated disorder versus correlated noise: Ordering in active systems

What the math gives to ML

The paper identifies a transferable mechanism in which long-range correlated quenched disorder, unlike temporally refreshed noise, can induce global ordering and qualitatively change relaxation exponents. The effect is controlled by the disorder's transversality, with continuous nonuniversal exponents and transitions between ordered/disordered or strong-coupling/free regimes at fixed disorder and noise variance. A concrete neural analogue is a CNN or spatial state-space model whose feature maps receive a fixed, long-range-correlated transverse perturbation at every layer, rather than independent dropout-like noise. The transfer is valuable if it produces measurable finite-size ordering, a tunable transition as the transverse fraction changes, and altered depth-relaxation exponents.