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arXiv · 2512.15493

Soft Geometric Inductive Bias for Object Centric Dynamics

Hampus Linander·Conor Heins·Alexander Tschantz·Marco Perin·Christopher Buckley
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Abstract

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.

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Hampus Linander, Conor Heins, Alexander Tschantz, Marco Perin, Christopher Buckley. 2025-12-17. Soft Geometric Inductive Bias for Object Centric Dynamics. https://arxiv.org/abs/2512.15493

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