Symplectic integrators for stabilizing deeper metriplectic dynamics

Determine whether using symplectic integrators (e.g., leapfrog or Störmer–Verlet) can stabilize deeper Hamiltonian–dissipative evolution in the Metriplector architecture compared to the current first-order Euler integration.

Background

For recognition tasks (e.g., CIFAR-100), Metriplector currently evolves fields via Euler integration under full metriplectic dynamics. Symplectic integrators preserve Hamiltonian structure and energy more faithfully, which could improve stability and enable deeper evolution. Establishing their efficacy within the coupled metriplectic setting is explicitly identified as an open question.

References

The architecture has not been tested at transformer scale, and significant open questions remain---notably whether symplectic integrators can stabilize deeper dynamics, and whether a single architecture can span all four domains.

— Metriplector: From Field Theory to Neural Architecture  (2603.29496 - Oprisa et al., 31 Mar 2026) in Section 8, Conclusion