通过对比实现等变性：从无标签有限群作用中学习可辨识的等变嵌入

我们提出了通过对比实现等变性（Equivariance by Contrast, EbC）来从观察对$(\mathbf{y}, g \cdot \mathbf{y})$中学习等变嵌入，其中$g$从作用于数据的有限群中抽取。我们的方法同时学习潜在空间和群表示，在该空间和表示中，群作用对应于可逆线性映射——而无需依赖于特定于群的归纳偏置。我们在由有限群$G:= (R_m \times \mathbb{Z}_n \times \mathbb{Z}_n)$定义的结构变换构成的无限dSprites数据集上验证了我们的方法，该群组合离散旋转和周期平移。 resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group $O(n)$ and the general linear group $GL(n)$. We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial非阿贝尔群和一个受计算机视觉中仿射等变性建模激励的乘积群。