Dynamic categories, dynamic operads: From deep learning to prediction markets

B. Shapiro, David I. Spivak
{"title":"Dynamic categories, dynamic operads: From deep learning to prediction markets","authors":"B. Shapiro, David I. Spivak","doi":"10.48550/arXiv.2205.03906","DOIUrl":null,"url":null,"abstract":"Natural organized systems adapt to internal and external pressures and this seems to happens all the way down. Wanting to think clearly about this idea motivates our paper, and so the idea is elaborated extensively in the introduction, which should be broadly accessible to a philosophically-interested audience. In the remaining sections, we turn to more compressed category theory. We define the monoidal double category O rg of dynamic organizations, we provide definitions of O rg -enriched, or dynamic , categorical structures—e.g. dynamic categories, operads, and monoidal categories—and we show how they instantiate the motivating philo-sophical ideas. We give two examples of dynamic categorical structures: prediction markets as a dynamic operad and deep learning as a dynamic monoidal category.","PeriodicalId":11810,"journal":{"name":"essentia law Merchant Shipping Act 1995","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"essentia law Merchant Shipping Act 1995","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2205.03906","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1

Abstract

Natural organized systems adapt to internal and external pressures and this seems to happens all the way down. Wanting to think clearly about this idea motivates our paper, and so the idea is elaborated extensively in the introduction, which should be broadly accessible to a philosophically-interested audience. In the remaining sections, we turn to more compressed category theory. We define the monoidal double category O rg of dynamic organizations, we provide definitions of O rg -enriched, or dynamic , categorical structures—e.g. dynamic categories, operads, and monoidal categories—and we show how they instantiate the motivating philo-sophical ideas. We give two examples of dynamic categorical structures: prediction markets as a dynamic operad and deep learning as a dynamic monoidal category.
动态分类,动态操作:从深度学习到预测市场
自然有组织的系统适应内部和外部压力,这似乎一直在发生。想要清楚地思考这个想法激发了我们的论文,所以这个想法在引言中得到了广泛的阐述,这应该是对哲学感兴趣的读者所能广泛理解的。在剩下的部分中,我们将转向更压缩的范畴论。我们定义了动态组织的单一元双范畴O rg,我们提供了O rg丰富的或动态的范畴结构的定义-例如。动态范畴、操作符和一元范畴——我们展示了它们如何实例化激励哲学思想。我们给出了两个动态分类结构的例子:预测市场作为一个动态操作,深度学习作为一个动态一元分类。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
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