Soft Geometric Inductive Bias for Object Centric Dynamics

TL;DR

This paper introduces object-centric world models using geometric algebra neural networks that incorporate a soft geometric inductive bias, improving long-term physical prediction accuracy in simulated 2D rigid body environments.

Contribution

It presents a novel approach combining geometric algebra with neural networks to provide a soft equivariance bias, enhancing object-centric dynamics modeling.

Findings

Better long-horizon prediction accuracy with soft geometric bias

Improved physical fidelity over non-equivariant models

Sample-efficient modeling of multi-object scenes

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.