Algebraic Invariant Quadratization Schemes for Cahn--Hilliard Equations

What the math gives to ML

The paper gives a constructive method for lifting rational-like computations into a larger state space with explicit algebraic constraints. Its transferable asset is the Jacobian-based tangent update that keeps auxiliary variables on the constraint manifold while the primary state evolves. This can become a constrained residual or recurrent layer in which rational features remain algebraically consistent over many layers instead of drifting under discretization. The most useful initial target is a deep residual MLP or neural state-space model using rational activations, with projection and constraint-residual ablations.