ERLHS: A Hamiltonian Framework for Coherence-Preserving Machine Intelligence

Current large language models (LLMs) operate without geometric or physical constraints on their latent dynamics. As a consequence, arbitrary textual perturbations—including prompt injection attacks—can drive their internal states into regions never encountered during training, resulting in incoherence, contradiction, and a lack of robust continual learning. We introduce ERLHS (Externally-Regularized Latent Hamiltonian Systems), a framework in which latent representations evolve on a smooth manifold equipped with a Hamiltonian coherence functional. Valid transitions are those that preserve or reduce this functional, providing a physically-motivated invariant that constrains updates. Version 1.1 (2026-04-23) — revisions: Section 1.2 reframed under the port-Hamiltonian formulation (van der Schaft & Jeltsema, 2014). Classical Hamiltonian dynamics conserve H exactly, but the paper's transition rule H(zt+1) ≤ H(zt) + ε permits controlled dissipation. Port-Hamiltonian systems accommodate both regimes via a Rayleigh-type operator R ⪰ 0, making the title “Hamiltonian Framework” technically accurate. Section 4.1 (Bounded Adversarial Influence) corrected. The v1.0 bound assumed Lipschitz continuity of H, which yields a lower bound on state displacement rather than the upper bound claimed. v1.1 uses a bi-Lipschitz (coercive-from-below) assumption that correctly gives ‖zt+1 − zt‖ ≤ α−1 ε. Bibliography: added van der Schaft & Jeltsema (2014) as reference for the port-Hamiltonian formalism. No changes to the core ERLHS framework, abstract conclusions, applications, or scope statement.