Universality of superdiffusion in simple random graphs

What the math gives to ML

The paper identifies a nontrivial universality mechanism: Bernoulli long-range disorder and the superdiffusive transport it creates are controlled by the same exponent, yet coarse-graining causes the long-range kinetic operator to dominate the disorder, recovering the clean Levy universality class. This suggests a sparse neural architecture with random power-law skip connections whose macroscopic information-propagation law is controlled by a single exponent rather than by the particular graph realization. The most direct test is to replace dense or local message passing with quenched sparse long-range residual propagation and measure whether propagation radius and spectral scaling follow the predicted Levy exponent while remaining stable across graph samples.