Any-dimensional equivariant neural networks
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917653160919040 |
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| author | Levin, Eitan Díaz, Mateo |
| author_facet | Levin, Eitan Díaz, Mateo |
| contents | Traditional supervised learning aims to learn an unknown mapping by fitting a function to a set of input-output pairs with a fixed dimension. The fitted function is then defined on inputs of the same dimension. However, in many settings, the unknown mapping takes inputs in any dimension; examples include graph parameters defined on graphs of any size and physics quantities defined on an arbitrary number of particles. We leverage a newly-discovered phenomenon in algebraic topology, called representation stability, to define equivariant neural networks that can be trained with data in a fixed dimension and then extended to accept inputs in any dimension. Our approach is user-friendly, requiring only the network architecture and the groups for equivariance, and can be combined with any training procedure. We provide a simple open-source implementation of our methods and offer preliminary numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06327 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Any-dimensional equivariant neural networks Levin, Eitan Díaz, Mateo Machine Learning Representation Theory Traditional supervised learning aims to learn an unknown mapping by fitting a function to a set of input-output pairs with a fixed dimension. The fitted function is then defined on inputs of the same dimension. However, in many settings, the unknown mapping takes inputs in any dimension; examples include graph parameters defined on graphs of any size and physics quantities defined on an arbitrary number of particles. We leverage a newly-discovered phenomenon in algebraic topology, called representation stability, to define equivariant neural networks that can be trained with data in a fixed dimension and then extended to accept inputs in any dimension. Our approach is user-friendly, requiring only the network architecture and the groups for equivariance, and can be combined with any training procedure. We provide a simple open-source implementation of our methods and offer preliminary numerical experiments. |
| title | Any-dimensional equivariant neural networks |
| topic | Machine Learning Representation Theory |
| url | https://arxiv.org/abs/2306.06327 |