物体中心ダイナミクスのためのソフトな幾何学的帰納バイアス
Soft Geometric Inductive Bias for Object Centric Dynamics
幾何代数ニューラルネットワークを用いて物体中心の世界モデルを構築し、厳密な等変性ではなくソフトな幾何学的帰納バイアスを与えることで、2D剛体ダイナミクスの長期予測において物理的忠実度が向上することを示した。
著者: Hampus Linander, Conor Heins, Alexander Tschantz, Marco Perin, Christopher Buckley
分類: cs.LG, cs.AI, stat.ML
原文アブストラクト
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.