Linear spreading speed in non-monotone population models

What the math gives to ML

The paper develops a constructive way to obtain stable macroscopic propagation from local, translation-equivariant, finite-range update rules even when the dynamics are non-monotone. Its transferable asset is the combination of coarse-grained good blocks, domination by supercritical oriented percolation, and shifted coupling that makes locally similar processes synchronize near their fronts despite different microscopic states. This suggests a neural cellular-automaton or recurrent-convolution architecture whose information propagation can be trained and empirically certified at block scale. The strongest first experiment is a robust signal-propagation regularizer for local recurrent networks, with explicit tests for survival, front speed, and synchronization under shared noise.