用几何代数构建有软对称先验的物体中心模型，提升物理动态预测精度。
Soft Geometric Inductive Bias for Object Centric Dynamics
- 采用几何代数神经网络实现物体中心建模，引入软几何先验
- 在长时序预测中，物理保真度优于非等变基线模型
- 适合需要样本高效、物理合理建模的多物体场景研究
等变性是学习物理动态的强大先验，但当对称性被破坏时，精确的群等变性可能降低性能。本文提出基于几何代数神经网络的物体中心世界模型，提供软几何归纳偏置。在包含静态障碍物的二维刚体动力学模拟环境中，模型通过自回归方式训练以预测下一步状态。在长时序推演中，相较于非等变基线模型，本方法在物理保真度上表现更优。该方法补充了近期软等变性思想，支持简单且精心设计的先验可实现稳健泛化。结果表明，几何代数为手工物理模型与无结构深度网络之间提供了有效折中，能生成适用于多物体场景的样本高效动态模型。
原文摘要 · Abstract (English)
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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