[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-116879-en":3,"doc-seo-116879-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},116879,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",8,"Research & Report","Towards fully covariant machine learning - Conceptual paper on passive symmetries","Any data representation rests on arbitrary investigator choices, producing exact passive symmetries that map one representation to another. The work analyzes passive symmetries relevant to machine learning, including graph relabeling (permutation symmetry) and the broader roles of coordinate freedom, gauge symmetry, and units covariance known from physics. It outlines dos and don’ts for practice that respects these symmetries, links the perspective to causal modeling, and argues benefits for out-of-sample generalization.","arXiv :2301 . 13724v2 [ stat .ML] 28 Jun 2023  \nTowards fully covariant machine learning  \nSoledad Villar∗  \nDepartment of Applied Mathematics and Statistics, Johns Hopkins University Baltimore MD, USA  \nDavid W. Hogg∗  \nCenter for Cosmology and Particle Physics, Department of Physics, New York University New York NY, USA  \nMax Planck Institute for Astronomy Heidelberg, Germany  \nFlatiron Institute, a division of the Simons Foundation New York NY, USA  \nWeichi Yao  \nDepartment of Technology, Operations, and Statistics, Stern School of Business, New York New York NY, USA  \nGeorge A. Kevrekidis  \nDepartment of Applied Mathematics and Statistics, Johns Hopkins University Baltimore MD, USA  \nLos Alamos National Laboratory  \nLos Alamos NM, USA  \nBernhard Schölkopf  \nMax Planck Institute for Intelligent Systems Tübingen, Germany  \n[soledad.villar@jhu. edu](soledad.villar@jhu. edu)  \n[david.hogg@nyu. edu](david.hogg@nyu. edu)  \n[wyao@stern.nyu. edu](wyao@stern.nyu. edu)[ ](wyao@stern.nyu. edu)University  \n[gkevrek1@jhu. edu](gkevrek1@jhu. edu)  \n[bs@tuebingen.mpg. de](bs@tuebingen.mpg. de)  \nAbstract  \nAny representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one possible representation to another. These are the passive symmetries; they include coordinate freedom, gauge symmetry, and units covariance, all of which have led to important results in physics. In machine learning, the most visible passive symmetry is the relabeling or permutation symmetry of graphs. Our goal is to understand the implications for machine learning of the many passive symmetries in play. We discuss dos and don’ts for machine learning practice if passive symmetries are to be respected. We discuss links to causal modeling, and argue that the implementation of passive symmetries is particularly valuable when the goal of the learning problem is to generalize out of sample. This paper is conceptual: It translates among the languages of physics, mathematics, and machine-learning. We believe that consideration and implementation of passive symmetries might help machine learning in the same ways that it transformed physics in the twentieth century.  \n∗equal first author  \n1 Introduction  \nMany important ideas in machine learning (ML) have come from—or been inspired by—mathematical physics. These include the kernel trick (Courant & Hilbert, 1953 ; Schölkopf & Smola, 2002) and the use of statistical mechanics techniques to solve probabilistic problems (Hastings, 1970 ; Gelfand, 2000) . Here we suggest another connection between physics and ML, which relates to the representation of observables: When features and labels are represented in a mathematical form that involves investigator choices, methods of ML (or any relevant model, relationship, method, or function) ought to be written in a form that is exactly equivariant to changes in those investigator choices. These ideas first appear in the physics literature in the 1910s (most famously in Einstein 1915) . They are given in the introduction of The Classical Groups (Weyl, 1946) asa motivation to study group theory. Literally the first sentences of Modern Classical Physics (Thorne & Blandford, 2017) are  \n[...] a central theme will be a Geometric Principle: The laws of physics must all be expressible as geometric (coordinate-independent and reference-frame-independent) relationships between geometric objects (scalars, vectors, tensors, ...) that represent physical entities.  \nThis Geometric Principle leads to the important physical symmetries of coordinate freedom and gauge symmetry; a small generalization would include what we will refer to as units covariance. Each of these symmetries has led to fundamental results in physics. Some of these ideas are also exploited in ML, in particular in the geometric deep learning literature (Bronstein et al. , ","cbCaiciPasO8RQho","https://ap.wps.com/l/cbCaiciPasO8RQho","pdf",811302,1,20,"English","en",105,"# Abstract\n# Introduction\n## Passive vs active symmetries\n## Units covariance\n## Motivation from physics and ML","[{\"question\":\"What are passive symmetries in this work, and why do they matter for machine learning?\",\"answer\":\"Passive symmetries arise from arbitrary investigator choices in data representation, creating exact transformations between equivalent representations. The paper argues ML models and methods should respect these symmetries to align with the underlying invariances.\"},{\"question\":\"How does graph node relabeling relate to the passive symmetries discussed?\",\"answer\":\"Graph relabeling is presented as an exact passive symmetry in ML, where functions on graphs should be equivariant to permutation of node labels. Graph neural network architectures build this symmetry into their design.\"},{\"question\":\"Why does the paper emphasize units covariance and generalization out of sample?\",\"answer\":\"Units covariance requires correct descriptions to use consistent input/output units and dimensions so numerical relationships remain valid. The paper argues implementing passive symmetries is especially valuable when the learning goal is to generalize beyond the training sample.\"}]","Towards fully covariant machine learning - Conceptual paper on passive symmetries | PDF",1785672192,50,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"towards-fully-covariant-machine-learning-conceptual-paper-on-passive-symmetries","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/towards-fully-covariant-machine-learning-conceptual-paper-on-passive-symmetries/116879/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What are passive symmetries in this work, and why do they matter for machine learning?","Question",{"text":75,"@type":76},"Passive symmetries arise from arbitrary investigator choices in data representation, creating exact transformations between equivalent representations. The paper argues ML models and methods should respect these symmetries to align with the underlying invariances.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does graph node relabeling relate to the passive symmetries discussed?",{"text":80,"@type":76},"Graph relabeling is presented as an exact passive symmetry in ML, where functions on graphs should be equivariant to permutation of node labels. Graph neural network architectures build this symmetry into their design.",{"name":82,"@type":73,"acceptedAnswer":83},"Why does the paper emphasize units covariance and generalization out of sample?",{"text":84,"@type":76},"Units covariance requires correct descriptions to use consistent input/output units and dimensions so numerical relationships remain valid. 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