DreamSAC: Learning Hamiltonian World Models via Symmetry Exploration

2026-03-08

AI Summary

Existing world models struggle to generalize to scenarios with novel physical properties because they rely solely on statistical correlations and fail to capture underlying generative principles such as symmetries and conservation laws. To address this limitation, this work proposes DreamSAC, a novel framework that integrates Hamiltonian-based curiosity-driven exploration to guide agents in actively collecting data rich in physical structure. Combined with self-supervised contrastive learning, DreamSAC extracts state representations from raw pixels that respect physical invariances. Notably, this approach is the first to implicitly embed conservation laws as priors within a world model, significantly enhancing its extrapolation performance in 3D physics simulation environments and outperforming current state-of-the-art baselines.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

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 \textbf{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, \textbf{DreamSAC}, trained on this actively curated data, significantly outperforms state-of-the-art baselines in 3D physics simulations on tasks requiring extrapolation.

Problem

• world models
• extrapolative generalization
• physical invariances
• conservation laws
• Hamiltonian dynamics

Innovation

• Symmetry Exploration
• Hamiltonian World Model
• Extrapolative Generalization
• Self-supervised Contrastive Learning
• Conservation Laws