Integrable building blocks for symplectic neural networks: learned-type layers, fiber-preserving layers, and what a single layer can do
Exactly symplectic neural networks are built almost exclusively from shear maps and gain expressivity only through depth. We ask what else a single explicit symplectic layer can be. Observing that every layer in use is the exact flow of a Hamiltonian that is a function of commuting integrals, we obtain three families of layers: a learned-type layer, in which every conjugate pair is rotated, squeezed or sheared by a state-dependent amount and the type is found by training; moving-plane shears, residual symplectic maps outside the known ridge-function class; and fiber-preserving layers, which combine an unconstrained point transformation with a fiber translation at the cost of one linear so...
| Authors | Andrew Qing He |
|---|---|
| Primary category | math.NA |
| Published | 18 October 2026 |
| Last updated at source | 18 October 2026 |
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