用几何代数设计轻量等变神经网络，提升泛化能力
GLGENN: A Novel Parameter-Light Equivariant Neural Networks Architecture Based on Clifford Geometric Algebras
- 基于几何代数设计权重共享机制，实现全伪正交变换等变
- 参数量显著减少，在多个基准任务上表现优于基线模型
- 适合需要高效等变建模的科研与工业场景
我们提出、实现并对比了基于几何（克莱夫福德）代数的新一代等变神经网络架构：广义利普希茨群等变神经网络（GLGENN）。该网络对任意非退化或退化的对称双线性形式下的向量空间的所有伪正交变换（包括旋转和反射）均保持等变性。通过引入考虑几何代数基本结构与运算的权重共享参数化方法，使GLGENN架构参数轻量，且过拟合倾向低于基线等变模型。在多个基准等变任务中，包括等变函数估计与凸包实验，GLGENN均表现优于或匹配现有竞争模型，同时使用显著更少的可优化参数。
原文摘要 · Abstract (English)
We propose, implement, and compare with competitors a new architecture of equivariant neural networks based on geometric (Clifford) algebras: Generalized Lipschitz Group Equivariant Neural Networks (GLGENN). These networks are equivariant to all pseudo-orthogonal transformations, including rotations and reflections, of a vector space with any non-degenerate or degenerate symmetric bilinear form. We propose a weight-sharing parametrization technique that takes into account the fundamental structures and operations of geometric algebras. Due to this technique, GLGENN architecture is parameter-light and has less tendency to overfitting than baseline equivariant models. GLGENN outperforms or matches competitors on several benchmarking equivariant tasks, including estimation of an equivariant function and a convex hull experiment, while using significantly fewer optimizable parameters.
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