[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84552-en":3,"doc-seo-84552-105":29,"detail-sidebar-cat-0-en-105":90},{"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":13,"seo_description":14,"update_tm":27,"read_time":28},84552,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","K-Inverse-RFM: A Modified RFM that Bridges the Gap to Neural Networks for Data-Corrupted Mathematical Tasks","This thesis presents K-Inverse-RFM, a modified Recursive Feature Machine (RFM) designed to narrow the performance and capability gap between RFM-style models and neural networks when mathematical tasks are corrupted by data issues. The work focuses on label noise and imbalanced data, and further studies how alternative data representations affect learning. Results compare K-Inverse-RFM to neural network baselines and synthesize findings across the studied corruption regimes.","arXiv :2607 .00329v 1 [ cs .LG] 1 Jul 2026  \nUNIVERSITY OF CALIFORNIA SAN DIEGO  \nK-Inverse-RFM: A Modified RFM that Bridges the Gap to Neural Networks for Data-Corrupted  \nMathematical Tasks  \nA Thesis submitted in partial satisfaction of the  \nrequirements for the degree Master of Science  \nin  \nComputer Science  \nby  \nGil Moshe Pasternak  \nCommittee in charge:  \nRamamohan Paturi, Chair  \nMikhail Belkin  \nTaylor Berg-Kirkpatrick  \nCopyright  \nGil Moshe Pasternak, 2025 All rights reserved.  \nThe Thesis of Gil Moshe Pasternak is approved, and it is acceptable in quality and form for publication on microfilm and electronically.  \nUniversity of California San Diego  \n2025  \nDEDICATION  \nTo my incredible parents, who moved 12,500 miles throughout their lives to provide me the opportunity to submit this Thesis Today  \nTo my sister for being a friend to grow up with  \nTo my maternal grandparents for their infinite love, support, and friendship  \nTo my paternal grandparents for their love-I hope I’ve made you proud To my great grandfather Michael, for paving a path to follow To Danielle, whose love pulls me through the harder days To Alec, Eric, John, Jesse, Alon, Assaf, Winkler: for endless support, advice, and laughter  \nTABLE OF CONTENTS  \nThesis Approval Page ........................................................... iii  \nDedication ..................................................................... iv  \nTable of Contents ............................................................... v  \nList [of Figures .................................................................. vi](of Figures .................................................................. vi)  \n[Acknowledgements .............................................................. viii](Acknowledgements .............................................................. viii)  \n[Abstract of the Thesis ........................................................... xi](Abstract of the Thesis ........................................................... xi)  \n[Chapter 1 Introduction ........................................................ 1](Chapter 1 Introduction ........................................................ 1)  \n[Chapter 2 Relevant Background ................................................ 3](Chapter 2 Relevant Background ................................................ 3)  \n[2.1 Kernels and Kernel Ridge Regression ...................................... 3](2.1 Kernels and Kernel Ridge Regression ...................................... 3)  \n[2.2 AGOP and the Neural Feature Ansatz ..................................... 5](2.2 AGOP and the Neural Feature Ansatz ..................................... 5)  \n[2.3 Recursive Feature Machines .............................................. 7](2.3 Recursive Feature Machines .............................................. 7)  \n[2.4 Grokking Modular Arithmetic ............................................ 8](2.4 Grokking Modular Arithmetic ............................................ 8)  \n[Chapter 3 The RFM-NN Gap .................................................. 10](Chapter 3 The RFM-NN Gap .................................................. 10)  \n[3.1 Label Noise ............................................................. 11](3.1 Label Noise ............................................................. 11)  \n[3.2 Imbalanced Data ........................................................ 13](3.2 Imbalanced Data ........................................................ 13)  \n3.2.1 Input and Output Imbalances ...................................... 13  \n3.2.2 Systematic Exclusion .............................................. 15  \n3.3 Alternative Data Representation .......................................... 16  \nChapter 4 Bridging the Gap: The K-Inverse-RFM ................................ 20  \n4.1 Method ................................................................ 20  \n4.2 Results .....................................................","cbCaidgVr3U2QSCQ","https://ap.wps.com/l/cbCaidgVr3U2QSCQ","pdf",10997330,1,46,"English","en",105,"# Chapter 1 Introduction\n# Chapter 2 Relevant Background\n## Kernels and Kernel Ridge Regression\n## AGOP and the Neural Feature Ansatz\n## Recursive Feature Machines\n## Grokking Modular Arithmetic\n# Chapter 3 The RFM-NN Gap\n## Label Noise\n## Imbalanced Data\n### Input and Output Imbalances\n### Systematic Exclusion\n## Alternative Data Representation\n# Chapter 4 Bridging the Gap: The K-Inverse-RFM\n## Method\n## Results\n### Label Noise\n### Imbalanced Data\n### Alternative Data Representation\n## Synthesis\n# Chapter 5 Conclusions, Limitations, and Future Avenues\n# Appendix A Interesting Observations on the Nature of Neural Networks\n## Neural Networks Learn Robust Features Early\n## Second Layer is for Specificity\n## The Relationship of Width and Role","[{\"question\":\"What problem does K-Inverse-RFM address in data-corrupted mathematical tasks?\",\"answer\":\"K-Inverse-RFM targets the gap between RFM-style models and neural networks under corrupted data conditions, especially focusing on label noise and imbalanced data. It aims to improve learning behavior in these challenging regimes.\"},{\"question\":\"Which data issues are analyzed in the thesis?\",\"answer\":\"The thesis analyzes label noise and imbalanced data. It further evaluates how alternative data representation choices change the learning outcome.\"},{\"question\":\"How does the thesis structure the comparison between RFM-based methods and neural networks?\",\"answer\":\"The document first reviews relevant background and then presents a dedicated chapter for the RFM–NN gap, followed by a chapter that introduces K-Inverse-RFM. Results are organized by the corruption type (label noise, imbalance, and representation).\"}]",1784196669,116,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"k-inverse-rfm-a-modified-rfm-that-bridges-the-gap-to-neural-networks-for-data-corrupted-mathematical-tasks","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/k-inverse-rfm-a-modified-rfm-that-bridges-the-gap-to-neural-networks-for-data-corrupted-mathematical-tasks/84552/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What problem does K-Inverse-RFM address in data-corrupted mathematical tasks?","Question",{"text":74,"@type":75},"K-Inverse-RFM targets the gap between RFM-style models and neural networks under corrupted data conditions, especially focusing on label noise and imbalanced data. It aims to improve learning behavior in these challenging regimes.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"Which data issues are analyzed in the thesis?",{"text":79,"@type":75},"The thesis analyzes label noise and imbalanced data. It further evaluates how alternative data representation choices change the learning outcome.",{"name":81,"@type":72,"acceptedAnswer":82},"How does the thesis structure the comparison between RFM-based methods and neural networks?",{"text":83,"@type":75},"The document first reviews relevant background and then presents a dedicated chapter for the RFM–NN gap, followed by a chapter that introduces K-Inverse-RFM. 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