# DreamSAC: Learning Hamiltonian World Models via Symmetry Exploration

arXiv: https://arxiv.org/abs/2603.07545 · HTML: https://mlsanity.com/paper/2603.07545/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 54 of its 60 references that are in the map.
- First posted on arXiv 8 Mar 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 30 of 54)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [What Makes for Good Views for Contrastive Learning?](https://mlsanity.com/paper/2005.10243/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Planning to Explore via Self-Supervised World Models](https://mlsanity.com/paper/2005.05960/) (2020)
- [Conditional Object-Centric Learning from Video](https://mlsanity.com/paper/2111.12594/) (2021)
- [How Far is Video Generation from World Model: A Physical Law Perspective](https://mlsanity.com/paper/2411.02385/) (2024)
- [A Survey on Self-supervised Learning: Algorithms, Applications, and Future Trends](https://mlsanity.com/paper/2301.05712/) (2023)
- [RoboDreamer: Learning Compositional World Models for Robot Imagination](https://mlsanity.com/paper/2404.12377/) (2024)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [DreamGen: Unlocking Generalization in Robot Learning through Video World Models](https://mlsanity.com/paper/2505.12705/) (2025)
- [WorldScore: A Unified Evaluation Benchmark for World Generation](https://mlsanity.com/paper/2504.00983/) (2025)
- [SlotFormer: Unsupervised Visual Dynamics Simulation with Object-Centric Models](https://mlsanity.com/paper/2210.05861/) (2022)
- [iVideoGPT: Interactive VideoGPTs are Scalable World Models](https://mlsanity.com/paper/2405.15223/) (2024)
- [Demystifying Contrastive Self-Supervised Learning: Invariances, Augmentations and Dataset Biases](https://mlsanity.com/paper/2007.13916/) (2020)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Discovering and Achieving Goals via World Models](https://mlsanity.com/paper/2110.09514/) (2021)
- [Entity Abstraction in Visual Model-Based Reinforcement Learning](https://mlsanity.com/paper/1910.12827/) (2019)
- [LieTransformer: Equivariant self-attention for Lie Groups](https://mlsanity.com/paper/2012.10885/) (2020)
- [Iso-Dream: Isolating and Leveraging Noncontrollable Visual Dynamics in World Models](https://mlsanity.com/paper/2205.13817/) (2022)
- [World-in-World: World Models in a Closed-Loop World](https://mlsanity.com/paper/2510.18135/) (2025)
- [Learning to Manipulate Anywhere: A Visual Generalizable Framework For Reinforcement Learning](https://mlsanity.com/paper/2407.15815/) (2024)
- [Differentiable Physics Models for Real-world Offline Model-based Reinforcement Learning](https://mlsanity.com/paper/2011.01734/) (2020)

## Built on by (most cited first, 1 of 1)

- [Back to Parsimonious Latents: Learning Task-Centric World Models from Visual Foundations](https://mlsanity.com/paper/2605.25620/) (2026)

## Abstract (arXiv)

Learned world models excel at interpolative generalization but fail at extrapolative generalization to novel physical properties. This limitation arises because they learn statistical correlations rather than the environment's underlying generative rules, such as physical invariances and conservation laws. We argue that learning these invariances is key to robust extrapolation. To achieve this, we first introduce Symmetry Exploration, an unsupervised exploration strategy where an agent is intrinsically motivated by a Hamiltonian-based curiosity bonus to actively probe and challenge its understanding of conservation laws, thereby collecting physically informative data. Second, we design a Hamiltonian-based world model that learns from the collected data, using a novel self-supervised contrastive objective to identify the invariant physical state from raw, view-dependent pixel observations. Our framework, DreamSAC, trained on this actively curated data, significantly outperforms state-of-the-art baselines in 3D physics simulations on tasks requiring extrapolation.