Categorical Equivariant Deep Learning: Category-Equivariant Neural Networks and Universal Approximation Theorems
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914216564228096 |
|---|---|
| author | Maruyama, Yoshihiro |
| author_facet | Maruyama, Yoshihiro |
| contents | We develop a theory of category-equivariant neural networks (CENNs) that unifies group/groupoid-equivariant networks, poset/lattice-equivariant networks, graph and sheaf neural networks. Equivariance is formulated as naturality in a topological category with Radon measures. Formulating linear and nonlinear layers in the categorical setup, we prove the equivariant universal approximation theorem in the general setting: the class of finite-depth CENNs is dense in the space of continuous equivariant transformations. We instantiate the framework for groups/groupoids, posets/lattices, graphs and cellular sheaves, deriving universal approximation theorems for them in a systematic manner. Categorical equivariant deep learning thus allows us to expand the horizons of equivariant deep learning beyond group actions, encompassing not only geometric symmetries but also contextual and compositional symmetries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categorical Equivariant Deep Learning: Category-Equivariant Neural Networks and Universal Approximation Theorems Maruyama, Yoshihiro Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition Robotics We develop a theory of category-equivariant neural networks (CENNs) that unifies group/groupoid-equivariant networks, poset/lattice-equivariant networks, graph and sheaf neural networks. Equivariance is formulated as naturality in a topological category with Radon measures. Formulating linear and nonlinear layers in the categorical setup, we prove the equivariant universal approximation theorem in the general setting: the class of finite-depth CENNs is dense in the space of continuous equivariant transformations. We instantiate the framework for groups/groupoids, posets/lattices, graphs and cellular sheaves, deriving universal approximation theorems for them in a systematic manner. Categorical equivariant deep learning thus allows us to expand the horizons of equivariant deep learning beyond group actions, encompassing not only geometric symmetries but also contextual and compositional symmetries. |
| title | Categorical Equivariant Deep Learning: Category-Equivariant Neural Networks and Universal Approximation Theorems |
| topic | Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition Robotics |
| url | https://arxiv.org/abs/2511.18417 |