[{"@context":"https:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/blog.terabox.com\/insights\/logup-zkvm-logarithmic-derivative-lookup#BlogPosting","mainEntityOfPage":"https:\/\/blog.terabox.com\/insights\/logup-zkvm-logarithmic-derivative-lookup","headline":"LogUp: Scaling ZKVMs with Logarithmic Derivatives","name":"LogUp: Scaling ZKVMs with Logarithmic Derivatives","description":"\ud83d\udcfa Today’s recommended deep-dive video: https:\/\/www.youtube.com\/watch?v=qv_5dF2_C4g Scaling ZKVMs with Logarithmic Derivatives: An Introduction to LogUpThe Evolution of Lookup ArgumentsThe LogUp BreakthroughPractical Performance and ImplementationKey TakeawaysQ&A Scaling ZKVMs with Logarithmic Derivatives: An Introduction to LogUp Traditional lookup arguments often struggle with... ","datePublished":"2026-08-11","dateModified":"2026-08-11","author":{"@type":"Person","@id":"https:\/\/blog.terabox.com\/author\/flextech-admin\/#Person","name":"flextech-admin","url":"https:\/\/blog.terabox.com\/author\/flextech-admin\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/ad516503a11cd5ca435acc9bb6523536?s=150&d=mm&r=gforcedefault=1","url":"https:\/\/secure.gravatar.com\/avatar\/ad516503a11cd5ca435acc9bb6523536?s=150&d=mm&r=gforcedefault=1","height":96,"width":96}},"publisher":{"@type":"Organization","name":"terabox","logo":{"@type":"ImageObject","@id":"http:\/\/blog.terabox.com\/wp-content\/uploads\/2021\/11\/logo\u4ea7\u54c1\u540d-\u7ad6\u7248.png","url":"http:\/\/blog.terabox.com\/wp-content\/uploads\/2021\/11\/logo\u4ea7\u54c1\u540d-\u7ad6\u7248.png","width":900,"height":900}},"image":{"@type":"ImageObject","@id":"https:\/\/blog.terabox.com\/wp-content\/uploads\/2026\/08\/mqdefault-1-1.jpg","url":"https:\/\/blog.terabox.com\/wp-content\/uploads\/2026\/08\/mqdefault-1-1.jpg","height":180,"width":320},"url":"https:\/\/blog.terabox.com\/insights\/logup-zkvm-logarithmic-derivative-lookup","video":{"@context":"http:\/\/schema.org\/","@type":"VideoObject","@id":"https:\/\/www.youtube.com\/watch?v=qv_5dF2_C4g#VideoObject","contentUrl":"https:\/\/www.youtube.com\/watch?v=qv_5dF2_C4g","name":"ZK9: logUp - Lookup arguments based on the logarithmic derivative - Ulrich Hab\u00f6ck","description":"This was recorded at the ZK9 - Zero Knowledge Summit 9 on April 4 2023 in Lisbon.\n\nhttps:\/\/www.zksummit.com\/\n\nTitle: logUp: Lookup arguments based on the logarithmic derivative\nSpeaker: Ulrich Hab\u00f6ck (Polygon Labs \/ Polygon Zero)\nDescription: Logarithmic derivatives translate products of linear factors into sums of their reciprocals, turning zeroes into simple poles of same multiplicity. Based on this simple fact, we describe a lookup argument which is particularly efficient in the \"batch-column\" setting, in which many columns are subject to one and the same table lookup.\n\nIf you like what we do:\n* Subscribe to our podcast newsletter - https:\/\/zeroknowledge.substack.com\n* Follow us on Twitter @zeroknowledgefm - https:\/\/twitter.com\/zeroknowledgefm\n* Join us on Telegram - https:\/\/zeroknowledge.fm\/telegram\n* Catch us on Youtube - https:\/\/zeroknowledge.fm\/\n* Head to the ZK Community Forum - https:\/\/community.zeroknowledge.fm\/\n* Support our Gitcoin Grant - https:\/\/zeroknowledge.fm\/gitcoin-grant-329-zkp-2","thumbnailUrl":["https:\/\/i.ytimg.com\/vi\/qv_5dF2_C4g\/default.jpg","https:\/\/i.ytimg.com\/vi\/qv_5dF2_C4g\/mqdefault.jpg","https:\/\/i.ytimg.com\/vi\/qv_5dF2_C4g\/hqdefault.jpg","https:\/\/i.ytimg.com\/vi\/qv_5dF2_C4g\/sddefault.jpg"],"uploadDate":"2023-04-15T08:00:25+00:00","duration":"PT31M31S","embedUrl":"https:\/\/www.youtube.com\/embed\/qv_5dF2_C4g","publisher":{"@type":"Organization","@id":"https:\/\/www.youtube.com\/channel\/UCYWsYz5cKw4wZ9Mpe4kuM_g#Organization","url":"https:\/\/www.youtube.com\/channel\/UCYWsYz5cKw4wZ9Mpe4kuM_g","name":"Zero Knowledge","description":"If you want to learn about zero knowledge proofs, advanced cryptography and privacy #zeroknowledge tech, you have come to the right place! \n\nWe post our podcast episodes here as well as event, study club, zk whiteboard sessions, educational material and more. find out more about us https:\/\/linktr.ee\/zeroknowledge\n\nWe also include content from our partners ZKHack and ZKV! \n\n\n","logo":{"url":"https:\/\/yt3.ggpht.com\/ytc\/AIdro_kbnDwtDnAU9oN-gcWRYWHa5JC7lEvtkWSaoaEcxhF_IZo=s800-c-k-c0x00ffffff-no-rj","width":800,"height":800,"@type":"ImageObject","@id":"https:\/\/www.youtube.com\/watch?v=qv_5dF2_C4g#VideoObject_publisher_logo_ImageObject"}},"potentialAction":{"@type":"SeekToAction","@id":"https:\/\/www.youtube.com\/watch?v=qv_5dF2_C4g#VideoObject_potentialAction","target":"https:\/\/www.youtube.com\/watch?v=qv_5dF2_C4g&t={seek_to_second_number}","startOffset-input":"required name=seek_to_second_number"},"interactionStatistic":[[{"@type":"InteractionCounter","@id":"https:\/\/www.youtube.com\/watch?v=qv_5dF2_C4g#VideoObject_interactionStatistic_WatchAction","interactionType":{"@type":"WatchAction"},"userInteractionCount":1500}],{"@type":"InteractionCounter","@id":"https:\/\/www.youtube.com\/watch?v=qv_5dF2_C4g#VideoObject_interactionStatistic_LikeAction","interactionType":{"@type":"LikeAction"},"userInteractionCount":30}]},"about":["Insights","\u300eEnglish\u300f"],"wordCount":1352},{"@context":"https:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Insights","item":"https:\/\/blog.terabox.com\/insights\/#breadcrumbitem"},{"@type":"ListItem","position":2,"name":"LogUp: Scaling ZKVMs with Logarithmic Derivatives","item":"https:\/\/blog.terabox.com\/insights\/logup-zkvm-logarithmic-derivative-lookup#breadcrumbitem"}]}]