Ghost-free higher-gradient Newtonian gravity from the Second Law of Thermodynamics

What the math gives to ML

The paper derives higher-gradient field dynamics from a concave entropy rather than a higher-time-derivative Lagrangian, yielding a first-order gradient flow with a Lyapunov function and a negative relaxation spectrum. The transferable asset is a principled way to add second- and third-spatial-derivative penalties to deep residual dynamics without introducing oscillatory or exponentially growing modes. A neural implementation can treat token position, graph nodes, or layer depth as a discrete spatial coordinate and replace an unconstrained residual update with an entropy-increasing, higher-gradient-damped update. This is most promising for deep residual stacks and sequence-state modules where long-range oscillations and Jacobian instability are failure modes.