We embed Hamiltonian/symplectic geometry by making the RNN state dynamics a symplectomorphism, which preserves Legendre duality (information geometry) through time. This yields structure-preserving representations enforced by the latent dynamics, rather than imposed indirectly via the output. （2/2）

Representation learning often emphasizes metric preservation. We instead build Symplectic structural invariance directly into the representation. （1/2）