单项矩阵组等变量神经功能网络

Hoang V. Tran, Thieu N. Vo, Tho H. Tran, An T. Nguyen, Tan Minh Nguyen
{"title":"单项矩阵组等变量神经功能网络","authors":"Hoang V. Tran, Thieu N. Vo, Tho H. Tran, An T. Nguyen, Tan Minh Nguyen","doi":"arxiv-2409.11697","DOIUrl":null,"url":null,"abstract":"Neural functional networks (NFNs) have recently gained significant attention\ndue to their diverse applications, ranging from predicting network\ngeneralization and network editing to classifying implicit neural\nrepresentation. Previous NFN designs often depend on permutation symmetries in\nneural networks' weights, which traditionally arise from the unordered\narrangement of neurons in hidden layers. However, these designs do not take\ninto account the weight scaling symmetries of $\\operatorname{ReLU}$ networks,\nand the weight sign flipping symmetries of $\\operatorname{sin}$ or\n$\\operatorname{tanh}$ networks. In this paper, we extend the study of the group\naction on the network weights from the group of permutation matrices to the\ngroup of monomial matrices by incorporating scaling/sign-flipping symmetries.\nParticularly, we encode these scaling/sign-flipping symmetries by designing our\ncorresponding equivariant and invariant layers. We name our new family of NFNs\nthe Monomial Matrix Group Equivariant Neural Functional Networks\n(Monomial-NFN). Because of the expansion of the symmetries, Monomial-NFN has\nmuch fewer independent trainable parameters compared to the baseline NFNs in\nthe literature, thus enhancing the model's efficiency. Moreover, for fully\nconnected and convolutional neural networks, we theoretically prove that all\ngroups that leave these networks invariant while acting on their weight spaces\nare some subgroups of the monomial matrix group. We provide empirical evidences\nto demonstrate the advantages of our model over existing baselines, achieving\ncompetitive performance and efficiency.","PeriodicalId":501301,"journal":{"name":"arXiv - CS - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Monomial Matrix Group Equivariant Neural Functional Networks\",\"authors\":\"Hoang V. Tran, Thieu N. Vo, Tho H. Tran, An T. Nguyen, Tan Minh Nguyen\",\"doi\":\"arxiv-2409.11697\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Neural functional networks (NFNs) have recently gained significant attention\\ndue to their diverse applications, ranging from predicting network\\ngeneralization and network editing to classifying implicit neural\\nrepresentation. Previous NFN designs often depend on permutation symmetries in\\nneural networks' weights, which traditionally arise from the unordered\\narrangement of neurons in hidden layers. However, these designs do not take\\ninto account the weight scaling symmetries of $\\\\operatorname{ReLU}$ networks,\\nand the weight sign flipping symmetries of $\\\\operatorname{sin}$ or\\n$\\\\operatorname{tanh}$ networks. In this paper, we extend the study of the group\\naction on the network weights from the group of permutation matrices to the\\ngroup of monomial matrices by incorporating scaling/sign-flipping symmetries.\\nParticularly, we encode these scaling/sign-flipping symmetries by designing our\\ncorresponding equivariant and invariant layers. We name our new family of NFNs\\nthe Monomial Matrix Group Equivariant Neural Functional Networks\\n(Monomial-NFN). Because of the expansion of the symmetries, Monomial-NFN has\\nmuch fewer independent trainable parameters compared to the baseline NFNs in\\nthe literature, thus enhancing the model's efficiency. Moreover, for fully\\nconnected and convolutional neural networks, we theoretically prove that all\\ngroups that leave these networks invariant while acting on their weight spaces\\nare some subgroups of the monomial matrix group. We provide empirical evidences\\nto demonstrate the advantages of our model over existing baselines, achieving\\ncompetitive performance and efficiency.\",\"PeriodicalId\":501301,\"journal\":{\"name\":\"arXiv - CS - Machine Learning\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Machine Learning\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11697\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Machine Learning","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11697","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

最近,神经功能网络(NFN)因其多样化的应用而备受关注,这些应用包括预测网络泛化和网络编辑,以及对隐式神经表征进行分类。以往的 NFN 设计通常依赖于神经网络权重的排列对称性,而这种对称性传统上源于隐藏层中神经元的无序排列。然而,这些设计并没有考虑到 $\operatorname{ReLU}$ 网络的权重缩放对称性,以及 $\operatorname{sin}$ 或 $\operatorname{tanh}$ 网络的权重符号翻转对称性。特别是,我们通过设计相应的等变层和不变层来编码这些缩放/符号翻转对称性。我们将新的 NFN 系列命名为单项矩阵组等变神经功能网络(Monomial-NFN)。由于对称性的扩展,与文献中的基线 NFN 相比,Monomial-NFN 的独立可训练参数要少得多,从而提高了模型的效率。此外,对于全连接神经网络和卷积神经网络,我们从理论上证明了使这些网络在权重空间上保持不变的所有群都是单项式矩阵群的某些子群。我们提供了经验证据来证明我们的模型相对于现有基线的优势,实现了具有竞争力的性能和效率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Monomial Matrix Group Equivariant Neural Functional Networks
Neural functional networks (NFNs) have recently gained significant attention due to their diverse applications, ranging from predicting network generalization and network editing to classifying implicit neural representation. Previous NFN designs often depend on permutation symmetries in neural networks' weights, which traditionally arise from the unordered arrangement of neurons in hidden layers. However, these designs do not take into account the weight scaling symmetries of $\operatorname{ReLU}$ networks, and the weight sign flipping symmetries of $\operatorname{sin}$ or $\operatorname{tanh}$ networks. In this paper, we extend the study of the group action on the network weights from the group of permutation matrices to the group of monomial matrices by incorporating scaling/sign-flipping symmetries. Particularly, we encode these scaling/sign-flipping symmetries by designing our corresponding equivariant and invariant layers. We name our new family of NFNs the Monomial Matrix Group Equivariant Neural Functional Networks (Monomial-NFN). Because of the expansion of the symmetries, Monomial-NFN has much fewer independent trainable parameters compared to the baseline NFNs in the literature, thus enhancing the model's efficiency. Moreover, for fully connected and convolutional neural networks, we theoretically prove that all groups that leave these networks invariant while acting on their weight spaces are some subgroups of the monomial matrix group. We provide empirical evidences to demonstrate the advantages of our model over existing baselines, achieving competitive performance and efficiency.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信