Symplectic billiards as Minkowski billiards

What the math gives to ML

The paper supplies a discrete variational construction whose update preserves an explicitly derived symplectic two-form, rather than merely approximating a continuous Hamiltonian flow. Its transferable asset is the generating-function equation L_2(q,q_1)+L_1(q_1,q_2)=0, together with the Legendre-dual representation that turns conjugate momentum into a geometrically normalized covector. This suggests a reversible recurrent or state-space layer whose position-momentum update is obtained by solving a convex implicit equation and is constrained to preserve dq wedge dp, potentially improving long-horizon stability and reducing dynamical drift.