Soft Geometric Inductive Bias for Object Centric Dynamics

Soft geometric inductive bias in world models improves physical fidelity and sample efficiency, outperforming strictly equivariant and non-geometric baselines in complex 2D rigid-body dynamics.

This research introduces object-centric world models built with geometric algebra neural networks. These models employ a 'soft' geometric inductive bias, allowing for robust performance even when underlying symmetries are broken, as commonly occurs in real-world environments with boundaries, contact, and varied material properties. Evaluated on 2D rigid-body simulations, the soft-biased models achieve superior long-horizon rollout accuracy and higher sample efficiency compared to strictly equivariant or non-geometric counterparts, particularly in scenarios involving object-wall collisions. This approach suggests a promising middle ground between hand-crafted physics engines and unstructured deep learning, enhancing generalization for multi-object scenes.