将李群胚对称性引入神经网络，统一了不同几何结构的等变学习框架。
Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networks
- 基于李群胚构造卷积层，实现微分流形上的对称性保持
- 证明其与李代数胚等变网络在特定条件下等价
- 提出广义不变全局池化，适用于复杂对称结构
我们提出李群胚等变神经网络，作为最近提出的拓扑范畴等变神经网络在微分设置下的特例。该网络由李群胚提升卷积和李群胚卷积层构成，并证明对于合适的李群胚，其等价于特定的李代数胚等变神经网络。此外，我们描述了群胚不变的全局池化，作为群不变全局池化的推广。进一步地，我们表明上述每一层均为最近提出的可容许范畴等变层的特例，通过展示它们定义了连续特征函子间的连续自然变换。
原文摘要 · Abstract (English)
We introduce Lie groupoid equivariant neural networks as a specialization of recently proposed topological category-equivariant neural networks to the differentiable setting. Lie groupoid equivariant neural networks are composed from Lie groupoid lifting convolutions and Lie groupoid convolution layers, and we show how for suitable Lie groupoids they are equivalent to certain Lie algebroid-equivariant neural networks. We additionally describe groupoid invariant global pooling as a generalization of group invariant global pooling. Furthermore, we show that each of the aforementioned layers is a special case of recently introduced admissible category-equivariant layers by demonstrating that they define continuous natural transformations between continuous feature functors.
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