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About this paper
Yoshihiro Maruyama
A unified mathematical framework leverages category theory to generalize equivariant deep learning beyond group symmetries, encompassing diverse data structures like posets and sheaves. This work defines Category-Equivariant Neural Networks (CENNs) and provides a universal approximation theorem for their expressive power.
Key insights
- Category theory provides a powerful and unified language for describing various data structures and their intrinsic symmetries, extending beyond traditional group-theoretic equivariance.
- The concept of 'natural transformation' formally captures the essence of equivariance, allowing for the principled construction of neural network layers that respect these compositional and relational structures.
- Layers like 'category convolutions' can systematically aggregate information along categorical arrows, providing a general recipe for designing equivariant architectures applicable to groups, posets, sheaves, and more.
Summary by alphaXiv.
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