تقرير
Any-dimensional equivariant neural networks
| العنوان: | Any-dimensional equivariant neural networks |
|---|---|
| المؤلفون: | Levin, Eitan, Díaz, Mateo |
| المصدر: | International Conference on Artificial Intelligence and Statistics. PMLR, 2024. Available from https://proceedings.mlr.press/v238/levin24a.html |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics Statistics |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Mathematics - Representation Theory, Statistics - Machine Learning |
| الوصف: | 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. Comment: 21 pages, 2 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2306.06327 |
| رقم الأكسشن: | edsarx.2306.06327 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |