Soft Geometric Inductive Bias for Object Centric Dynamics
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908718335000576 |
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| author | Linander, Hampus Heins, Conor Tschantz, Alexander Perin, Marco Buckley, Christopher |
| author_facet | Linander, Hampus Heins, Conor Tschantz, Alexander Perin, Marco Buckley, Christopher |
| contents | Equivariance is a powerful prior for learning physical dynamics, yet exact group equivariance can degrade performance if the symmetries are broken. We propose object-centric world models built with geometric algebra neural networks, providing a soft geometric inductive bias. Our models are evaluated using simulated environments of 2d rigid body dynamics with static obstacles, where we train for next-step predictions autoregressively. For long-horizon rollouts we show that the soft inductive bias of our models results in better performance in terms of physical fidelity compared to non-equivariant baseline models. The approach complements recent soft-equivariance ideas and aligns with the view that simple, well-chosen priors can yield robust generalization. These results suggest that geometric algebra offers an effective middle ground between hand-crafted physics and unstructured deep nets, delivering sample-efficient dynamics models for multi-object scenes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Soft Geometric Inductive Bias for Object Centric Dynamics Linander, Hampus Heins, Conor Tschantz, Alexander Perin, Marco Buckley, Christopher Machine Learning Artificial Intelligence Equivariance is a powerful prior for learning physical dynamics, yet exact group equivariance can degrade performance if the symmetries are broken. We propose object-centric world models built with geometric algebra neural networks, providing a soft geometric inductive bias. Our models are evaluated using simulated environments of 2d rigid body dynamics with static obstacles, where we train for next-step predictions autoregressively. For long-horizon rollouts we show that the soft inductive bias of our models results in better performance in terms of physical fidelity compared to non-equivariant baseline models. The approach complements recent soft-equivariance ideas and aligns with the view that simple, well-chosen priors can yield robust generalization. These results suggest that geometric algebra offers an effective middle ground between hand-crafted physics and unstructured deep nets, delivering sample-efficient dynamics models for multi-object scenes. |
| title | Soft Geometric Inductive Bias for Object Centric Dynamics |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2512.15493 |