Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt

What the math gives to ML

The paper provides an exact mechanism by which microscopic decoherence renormalizes the effective interaction and field of a lattice population, while leaving strategic Gibbs fluctuations as a separate source of randomness. In particular, depolarization preserves the microscopic neutrality condition but suppresses the collective Ising coupling as $(1-p)^2$, producing a sharp transition from ordered coexistence to disordered crossover at a calculable noise level. The most transferable neural-network construction is a coupling-aware noise controller for binary energy-based models or recurrent attractor networks: estimate the effective interaction strength and tune injected noise to remain below, at, or above the collective critical boundary rather than treating noise as an arbitrary hyperparameter.