关于群等变算子通过置换测度的有限表示
群论
2022-03-11 v2 机器学习
表示论
摘要
对 -等变算子的研究对于解释和理解神经网络的架构具有极大意义。在本文中,我们证明每个线性 -等变算子均可由一个合适的置换测度生成,前提是群 在有限信号域 上传递作用。这一结果提供了一种在有限情形下构造线性 -等变算子的新方法。
引用
@article{arxiv.2008.06340,
title = {On the finite representation of group equivariant operators via permutant measures},
author = {Giovanni Bocchi and Stefano Botteghi and Martina Brasini and Patrizio Frosini and Nicola Quercioli},
journal= {arXiv preprint arXiv:2008.06340},
year = {2022}
}
备注
We have extended the introduction, providing more context about our approach, and the discussion. We have also added Section 4, showing possible advantages of the use of GENEOs built by permutant measures. The experiment described in Section 4 has been made by Giovanni Bocchi. For this reason, he has been added to the list of authors of the paper