HaM-World: Soft-Hamiltonian World Models with Selective Memory for Planning

HaM-World introduces a structured world model that combines history-conditioned selective memory with a Soft‑Hamiltonian latent dynamics prior. The model decomposes the latent state into a canonical (q,p) subspace governed by an energy‑derived Hamiltonian vector field and a context subspace c capturing non‑conservative factors, while Mamba selective state‑space memory conditions the transition used for prediction, reward, value estimation, and planning. Across six DeepMind Control Suite tasks, HaM-World achieves top rankings on four tasks, improves average AUC, reduces imagined‑rollout error by 45% on short‑to‑medium horizons, and outperforms baselines under 12 out‑of‑distribution perturbations.

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