Propagation rates in integro-differential equations of ignition type

What the math gives to ML

The paper identifies a precise mechanism by which heavy-tailed nonlocal transport changes propagation: the truncated first moment of the jump kernel determines whether influence travels linearly, polynomially faster, or at the critical rate t log t. This suggests replacing local residual mixing in deep sequence or graph models with a sparse heavy-tailed nonlocal operator whose receptive field grows predictably with depth. The transferable asset is not the PDE-specific ignition reaction, but the kernel-dependent propagation law and the convex-tail inequalities used to control profile shape. A first experiment should test whether the critical s = 1/2 kernel gives better long-range information transfer at fixed depth and FLOPs than local convolution or exponentially decaying mixing.