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

arXiv: https://arxiv.org/abs/2605.05951 · HTML: https://mlsanity.com/paper/2605.05951/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 50 of its 57 references that are in the map.
- First posted on arXiv 7 May 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)
- State-space sequence models (S4, Mamba) / [Video, motion and generative Mamba models](https://mlsanity.com/ssm/video-motion-and-generative-mamba-models/)

## Builds on (most cited first, 30 of 50)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Revisiting Feature Prediction for Learning Visual Representations from Video](https://mlsanity.com/paper/2404.08471/) (2024)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [Learning Interactive Real-World Simulators](https://mlsanity.com/paper/2310.06114/) (2023)
- [Learning Invariant Representations for Reinforcement Learning without Reconstruction](https://mlsanity.com/paper/2006.10742/) (2020)
- [Temporal Difference Learning for Model Predictive Control](https://mlsanity.com/paper/2203.04955/) (2022)
- [Planning to Explore via Self-Supervised World Models](https://mlsanity.com/paper/2005.05960/) (2020)
- [Transformers are Sample-Efficient World Models](https://mlsanity.com/paper/2209.00588/) (2022)
- [Diffusion for World Modeling: Visual Details Matter in Atari](https://mlsanity.com/paper/2405.12399/) (2024)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Understanding World or Predicting Future? A Comprehensive Survey of World Models](https://mlsanity.com/paper/2411.14499/) (2024)
- [iVideoGPT: Interactive VideoGPTs are Scalable World Models](https://mlsanity.com/paper/2405.15223/) (2024)
- [Structured State Space Models for In-Context Reinforcement Learning](https://mlsanity.com/paper/2303.03982/) (2023)
- [STORM: Efficient Stochastic Transformer based World Models for Reinforcement Learning](https://mlsanity.com/paper/2310.09615/) (2023)
- [DreamerPro: Reconstruction-Free Model-Based Reinforcement Learning with Prototypical Representations](https://mlsanity.com/paper/2110.14565/) (2021)

## Built on by (most cited first, 2 of 2)

- [MOSH-WM: Mask-Grounded Soft-Hamiltonian Dynamics for Object-Centric World Models](https://mlsanity.com/paper/2608.22750/) (2026)
- [LeHami: Symplectic Latent Dynamics for World Models](https://mlsanity.com/paper/2610.15267/) (2026)

## Abstract (arXiv)

World models support model-based planning through learned latent dynamics, but imagined rollouts can become unstable as the planning horizon grows or the dynamics distribution shifts. We propose HaM-World, a structured world model that combines history-conditioned selective memory with a Soft-Hamiltonian latent dynamics prior. The latent state is decomposed into a canonical (q,p) subspace and a context subspace c. Mamba selective state-space memory summarizes past observations and actions and conditions the same latent transition used for prediction, reward and value estimation, imagined rollouts, and cross-entropy method planning. The (q,p) subspace follows an energy-derived Hamiltonian vector field augmented with learnable residual and control dynamics, while c represents semantic, dissipative, and other non-conservative factors. On six DeepMind Control Suite tasks, HaM-World ranks first on four tasks and second on two, achieving the highest average AUC on the four-task core suite (117.9, 9.5% above TD-MPC2). Within the short-to-medium horizons used by the planner, it reduces imagined-rollout error to 45% of a strong baseline and wins 11 of 12 rollout-MSE cells for horizons k in {3,5,7}. At longer open-loop horizons, its error grows faster and is overtaken between k=7 and k=20; we therefore do not claim uniform long-horizon stability. Under 12 out-of-distribution perturbations involving dynamics shifts, action delay, and observation masking, it achieves the highest absolute return in every condition, with average gains of 10.2% on Finger Spin and 13.6% on Reacher Easy. Ablations show that memory accounts for the larger share of the observed gains, while Soft-Hamiltonian geometry provides smaller but consistent complementary improvements.