集成学习通过数据增强自动获得群等变性，无需依赖特定网络极限。
Ensembles provably learn equivariance through data augmentation
- 不依赖神经正切核极限，证明集成可自发学习等变性
- 在随机设置和多种架构下仍保持等变性涌现
- 适用于图像、点云等需要对称性建模的任务
近期研究证明，在无限宽神经网络的极限下，通过完整数据增强，神经网络集成会自然产生群等变性。本文显著拓展了该结论：我们证明这种等变性涌现并不依赖神经正切核极限；同时考虑了随机设置，并推广到更一般架构。对于后者，我们给出一个关于架构与群作用关系的简单充分条件，确保结果成立。通过简单的数值实验验证了理论发现。
原文摘要 · Abstract (English)
Recently, it was proved that group equivariance emerges in ensembles of neural networks as the result of full augmentation in the limit of infinitely wide neural networks (neural tangent kernel limit). In this paper, we extend this result significantly. We provide a proof that this emergence does not depend on the neural tangent kernel limit at all. We also consider stochastic settings, and furthermore general architectures. For the latter, we provide a simple sufficient condition on the relation between the architecture and the action of the group for our results to hold. We validate our findings through simple numeric experiments.
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