Boosting Deep Neural Networks with Geometrical Prior Knowledge: A Survey

Boosting Deep Neural Networks with Geometrical Prior Knowledge: A Survey | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Boosting Deep Neural Networks with Geometrical Prior Knowledge: A Survey Matthias Rath, Alexandru Paul Condurache This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2649096/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Mar, 2024 Read the published version in Artificial Intelligence Review → Version 1 posted 7 You are reading this latest preprint version Abstract Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive and time-consuming. Additionally, assessing the networks' generalization abilities or predicting how the inferred output changes under input transformations is complicated since the networks are usually treated as a black box. Both of these problems can be mitigated by incorporating prior knowledge into the neural network. One promising approach, inspired by the success of convolutional neural networks in computer vision tasks, is to incorporate knowledge about symmetric geometrical transformations of the problem to solve that affect the output in a predictable way. This promises an increased data efficiency and more interpretable network outputs. In this survey, we try to give a concise overview about different approaches that incorporate geometrical prior knowledge into neural networks. Additionally, we connect those methods to 3D object detection for autonomous driving, where we expect promising results when applying those methods. Invariance Equivariance Group Theory Geometrical Prior Knowledge Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 19 Mar, 2024 Read the published version in Artificial Intelligence Review → Version 1 posted Editorial decision: Major revision 09 May, 2023 Reviews received at journal 11 Apr, 2023 Reviewers agreed at journal 02 Apr, 2023 Reviewers invited by journal 02 Apr, 2023 Editor assigned by journal 09 Mar, 2023 Submission checks completed at journal 03 Mar, 2023 First submitted to journal 02 Mar, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2649096","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":180602620,"identity":"7f21ae8c-4454-4d9a-b832-2804d9408057","order_by":0,"name":"Matthias Rath","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAElEQVRIiWNgGAWjYJACZgYDGKOCmYFBAshibMCrgbEZqgXIOEO0FgaoFsY2IrTotp8//rigwM6eQfrw88eF86zlGKSbD3/4uYNBnl/sAFYtZmeSGZtnGCQnNvClGTbP3JZuzCBzLE2y9wyD4czZCdi1HABq4TFgTmDgYTBs5t12OLFBIseMmbGNIcHgNg4t5x+DtNTbM/Cwf2zmnXO4HqjF+DNeLTfAthxmbODhAdrScDiBQSLHQBq/lseGs3kMjie28fAUzuY5lm7YBvZLmwRuv5xPfPCZ50+1PT8P+4bPPDXW8vzgEGuzATKwa4EDNjSGBH7lo2AUjIJRMArwAgCAJVTvBjM5EgAAAABJRU5ErkJggg==","orcid":"","institution":"Robert Bosch (Germany)","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Matthias","middleName":"","lastName":"Rath","suffix":""},{"id":180602621,"identity":"16adf2ed-f364-4c5b-8565-f91b355ed76f","order_by":1,"name":"Alexandru Paul Condurache","email":"","orcid":"","institution":"Robert Bosch (Germany)","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Alexandru","middleName":"Paul","lastName":"Condurache","suffix":""}],"badges":[],"createdAt":"2023-03-02 22:44:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2649096/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2649096/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10462-024-10722-5","type":"published","date":"2024-03-19T15:03:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":53403937,"identity":"48fe0102-6f32-49e4-aa60-b8b0f5d32721","added_by":"auto","created_at":"2024-03-25 15:16:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":758897,"visible":true,"origin":"","legend":"","description":"","filename":"00surveyUpload.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2649096/v1_covered_c8550f61-8d3d-4e30-94c1-755d61c0f62f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Boosting Deep Neural Networks with Geometrical Prior Knowledge: A Survey","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"artificial-intelligence-review","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"aire","sideBox":"Learn more about [Artificial Intelligence Review](http://link.springer.com/journal/10462)","snPcode":"10462","submissionUrl":"https://submission.nature.com/new-submission/10462/3","title":"Artificial Intelligence Review","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Invariance, Equivariance, Group Theory, Geometrical Prior Knowledge","lastPublishedDoi":"10.21203/rs.3.rs-2649096/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2649096/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. 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