Deterministic cascade coarsening in a Bistable Gene Toggle model

What the math gives to ML

The paper identifies a nonstandard coarsening mechanism in which interfaces remain pinned and then disappear through abrupt collective cascades rather than moving by smooth curvature flow. Its transferable asset is the combination of metastable bistability, local diffusive coupling, and discrete scale invariance: cascade times are geometrically spaced and observables show log-periodic modulation of a power law. A neural analogue can be built as a spatially coupled bistable latent layer for image or grid-structured prediction, with an event-driven inference schedule that detects and exploits these cascades. The key falsifiable test is whether interface density and cascade observables exhibit geometric cascade timing and a log-periodic residual, rather than ordinary Allen–Cahn scaling.