Opening the Black Box: predicting the trainability of deep neural networks with reconstruction entropy

Opening the Black Box: predicting the trainability of deep neural networks with reconstruction entropy | 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 Article Opening the Black Box: predicting the trainability of deep neural networks with reconstruction entropy Johanna Erdmenger, Yanick Thurn, Ro Jefferson This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4737447/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract An important challenge in machine learning is to predict the initial conditions under which a given neural network will be trainable. We present a method for predicting the trainable regime in parameter space for deep feedforward neural networks, based on reconstructing the input from subsequent activation layers via a cascade of single-layer auxiliary networks. For both MNIST and CIFAR10, we show that a single epoch of training of the shallow cascade networks is sufficient to predict the trainability of the deep feedforward network, thereby providing a significant reduction in overall training time. We achieve this by computing the relative entropy between reconstructed images and the original inputs, and show that this probe of information loss is sensitive to the phase behaviour of the network. Moreover, our approach illustrates the network's decision making process by displaying the changes performed on the input data at each layer. Our results provide a concrete link between the flow of information and the trainability of deep neural networks, further explaining the role of criticality in these systems. Physical sciences/Mathematics and computing/Computer science Physical sciences/Physics/Information theory and computation Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-4737447","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":330272927,"identity":"dc971afe-916c-4536-aef4-b5423b254a8e","order_by":0,"name":"Johanna Erdmenger","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0003-4776-4326","institution":"Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität Würzburg","correspondingAuthor":true,"prefix":"","firstName":"Johanna","middleName":"","lastName":"Erdmenger","suffix":""},{"id":330272928,"identity":"1858a9c3-022e-4ad6-ad34-966766357209","order_by":1,"name":"Yanick Thurn","email":"","orcid":"https://orcid.org/0000-0001-8242-3362","institution":"Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universität Würzburg","correspondingAuthor":false,"prefix":"","firstName":"Yanick","middleName":"","lastName":"Thurn","suffix":""},{"id":330272929,"identity":"2e230b50-83af-4d85-8129-09c7a5a40ad0","order_by":2,"name":"Ro Jefferson","email":"","orcid":"","institution":"Institute for Theoretical Physics, and Department of Information and Computing Sciences, Utrecht University","correspondingAuthor":false,"prefix":"","firstName":"Ro","middleName":"","lastName":"Jefferson","suffix":""}],"badges":[],"createdAt":"2024-07-14 07:30:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4737447/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4737447/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":62905956,"identity":"2e76228f-5a8d-43e7-941f-3cd859b603e2","added_by":"auto","created_at":"2024-08-21 01:23:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":953551,"visible":true,"origin":"","legend":"","description":"","filename":"ReconstructionEntropy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4737447/v1_covered_4435b848-aae3-4dcc-9ece-db335f3d4d13.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Opening the Black Box: predicting the trainability of deep neural networks with reconstruction entropy","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4737447/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4737447/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"An important challenge in machine learning is to predict the initial conditions under which a given neural network will be trainable. 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