对比等变性：从无标注有限群作用中学习可辨识的等变嵌入
Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actions
AI总结：
本文提出对比等变性（EbC）方法，从无标注有限群作用观测对中学习可辨识的等变嵌入，无需特定群归纳偏置，并在合成数据上验证了非阿贝尔群及乘积群的有效性。
摘要：
我们提出对比等变性（Equivariance by Contrast, EbC）方法，从观测对 $(\mathbf{y}, g \cdot \mathbf{y})$ 中学习等变嵌入，其中 $g$ 取自作用于数据的有限群。我们的方法联合学习一个潜在空间和一个群表示，在该表示中群作用对应于可逆线性映射——无需依赖特定群的归纳偏置。我们在无限 dSprites 数据集上验证了该方法，该数据集包含由有限群 $G:= (R_m \times \mathbb{Z}_n \times \mathbb{Z}_n)$ 定义的结构化变换，结合了离散旋转和周期平移。所得的嵌入展现出高保真度的等变性，群操作在潜在空间中被忠实地复现。在合成数据上，我们进一步在非阿贝尔正交群 $O(n)$ 和一般线性群 $GL(n)$ 上验证了该方法。我们还提供了可辨识性的理论证明。尽管在真实世界数据上对多种群类型进行广泛评估仍是未来工作，但我们的结果首次成功展示了仅从群作用观测中进行通用编码器式等变学习，包括非平凡的非阿贝尔群以及一个受计算机视觉中仿射等变性建模启发的乘积群。
英文摘要：
We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs $(\mathbf{y}, g \cdot \mathbf{y})$, where $g$ is drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps -- without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group $G:= (R_m \times \mathbb{Z}_n \times \mathbb{Z}_n)$, combining discrete rotations and periodic translations. The 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 non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
