arXiv：cs.AI· Romina Yalovetzky, Randall Balestriero, Yann LeCun·· 16 小时前
LeHami：为世界模型引入辛几何隐动力学
LeHami: Symplectic Latent Dynamics for World Models
AI 导读
研究团队提出 Symplectic Hamiltonian JEPA（LeHami），用动作条件化的 Hamiltonian 流替换 JEPA 的标准预测器，在结构化隐状态 (q, p) 上以精确辛 leapfrog 步积分，从而在任意 rollout 步保持相空间体积、排除潜分布均匀收缩与不同隐状态合并。
正文
Abstract:Joint-embedding predictive architectures (JEPAs) learn world models directly in latent space, but unconstrained autoregressive predictors may contract the latent distribution over long rollouts. We introduce Symplectic Hamiltonian JEPA (LeHami), which replaces the standard predictor with an action-conditioned Hamiltonian flow over a structured latent state (q, p) integrated using an exactly symplectic leapfrog step. This construction preserves phase-space volume at every rollout step and rules out uniform contraction, asymptotically stable fixed points, and merging of distinct latent states, independently of the learned parameters or action sequence. We obtain the momentum-like component from temporal derivatives of the learned position-like representation, providing an explicit second-order state for prediction and control. On conservative and actuated visual pendulum environments, LeHami substantially improves long-horizon velocity prediction over an unconstrained JEPA world model and empirically maintains constant latent volume where the baseline contracts. The learned flow also supports accurate integration at unseen sub-frame step sizes and numerical time reversal. These results show how geometric structure can provide inference-time guarantees that are complementary to representation regularization in latent world models.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Robotics (cs.RO) |
| Cite as: | arXiv:2610.15267 [cs.LG] |
| (or arXiv:2610.15267v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.15267 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Romina Yalovetzky [view email]
[v1]
Sun, 11 Oct 2026 01:28:41 UTC (3,897 KB)
来源：arXiv：cs.AI · arxiv.org