[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-328141-105":59,"doc-detail-328141-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","at-grok-is-not-converged-a-measurement-validity-audit-for-grokking-representation-metrics","At-Grok Is Not Converged - A Measurement-Validity Audit for Grokking Representation Metrics","","On modular arithmetic, embedding-based representation metrics can keep compressing well after networks have already generalized, making transition-time readings overstate the converged circuit complexity by 3–5× and, for modular MLPs, even reverse the reported trend. Grokking studies often infer representation structure from a single snapshot, which is unsafe. The paper identifies two issues: a measurement hazard from effective-rank transients and a lag controlled by normalization and LayerNorm-only ablations.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/at-grok-is-not-converged-a-measurement-validity-audit-for-grokking-representation-metrics/328141/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/at-grok-is-not-converged-a-measurement-validity-audit-for-grokking-representation-metrics/328141.png","ImageObject",300,407,{"name":92,"@type":93},"Theodora","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What measurement hazard occurs when metrics are read at the grokking step (Tgrok)?","Question",{"text":112,"@type":113},"A representation metric such as embedding effective rank can be a transient that later training drives down to a low-rank floor. As a result, the at-grok value can overstate the converged complexity by about 3–5× and may erase qualitative distinctions on the MLP.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the paper distinguish onset time (Tgrok) from compression time (Tcompress)?",{"text":117,"@type":113},"It frames the audit to separate generalization onset (when test accuracy rises) from representation compression (when effective rank drops), and it flags censoring and boundary cells that did not fully generalize.",{"name":119,"@type":110,"acceptedAnswer":120},"What controls the lag between generalization onset and representation compression?",{"text":121,"@type":113},"A LayerNorm-only one-variable ablation shows the completed fraction of rank compression by the grok step can change substantially, enlarging the post-grok lag. The paper reports that a post-grok separation between onset and compression appears on every architecture tested and varies with the normalization scheme.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},328141,1791900395,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},687197207919,"https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552","arXiv :2607 .06639v 1 [ cs .LG] 7 Jul 2026  \nAt-Grok Is Not Converged: A Measurement-Validity Audit for Grokking Representation Metrics  \nTruong Xuan Khanh 1  \n1 H&K Research Studio / Clevix LLC, Hanoi, Vietnam  \n[khanh@clevix. vn](khanh@clevix. vn)  \nAbstract  \nOn modular arithmetic, a network’s embedding keeps compressing for tens of thousands of optimization steps after it has already generalized—so a value read at the grokking transition overstates the converged circuit by 3–5 × and, on the modular MLP, inverts the very trend it is used to report. A growing body of grokking research nonetheless reads representation structure from a single such snapshot and treats it as a property of the converged circuit. We show this is unsafe in two distinct ways, and supply the tooling to avoid it. First, a measurement hazard: the value of a standard representation metric — embedding effective rank — read atthe transition can be a transient that long training drives down to a low-rank floor. The atgrok value overstates the converged complexity (still 1 .3–1.5 × even on a transformer trained to convergence) and, on the MLP, erases the one qualitative distinction that matters: which cells compress at all. Contra readings in which low-rank compression coincides with the accuracy transition, compression lags it by a large amount (of order Tgrok , ≥ 104 steps) . Second, a positive finding about what controls that lag: in a one-variable ablation that adds LayerNormand nothing else, the fraction of rank compression already completed by the grok step moves from 0 .87 to 0 .25, enlarging the post-grok lag—so a post-grok separation between generalization onset and representation compression is present on every architecture we test, and its size is modulated by the normalization scheme. We package this as a measurement-validity audit that separates onset (Tgrok ) from compression (Tcompress ), flags censoring, gates boundary cells that did not fully generalize, verifies that the compression floor has itself plateaued (the same hazard can recur on the denominator), and declines an ordering verdict when the order statistic is undefined. The audit ships with an adversarial test suite that checks the reason behind each verdict—it caught a false-confidence regression during development—and a generic adapter that audits externally-logged runs without retraining. The transient and the lag both recur onevery architecture we test; a secondary, MLP-specific “depth law” relating the norm budget to the converged floor (Spearman −1 .0) fails a pre-registered generality test (transformer +0 . 14; protocol-reversed under free weight decay), and we report it as a negative result on generality (Appendix A) .  \n1 Introduction  \nGrokking — delayed generalization long after a network fits its training set [1] — is increasingly studied through the representation: the Fourier structure of embeddings [5], effective rank or spectral-entropy complexity [6], intrinsic dimension, and persistent homology [7] . A recurring  \nmove in this literature is to take a measurement at or near the grokking step—the moment test accuracy rises—and read it as a property of the generalizing circuit.  \nThis move has a failure mode that is easy to hit and hard to notice: the value of a representation metric at the grokking step need not be its converged value, and reading it can reverse the dependence one set out to characterize. On modular arithmetic we find a sharp instance. At grokking the embedding effective rank is uniformly high and barely separates across budgets at the low-budget end. The non-compressing boundary cell (ρ = 1 .00, which never compresses and stays at rank ≈ 42) and its strongly-compressing neighbour (ρ = 1 .05, which converges to rank ≈ 12) read almost identically at grok (≈ 46 vs. ≈ 48) . Stopping there, the natural reading is a high, flat“norm-controlled circuit complexity,” which is exactly backwards: training each fully-generalizing budget long past the transition ","cbCaiuJISVEp1H2d","https://ap.wps.com/l/cbCaiuJISVEp1H2d","pdf",577731,26,"English","# Abstract\n# Introduction\n## Measurement hazard at Tgrok\n## Compression lag and controls\n## Audit tooling and test suite","[{\"question\":\"What measurement hazard occurs when metrics are read at the grokking step (Tgrok)?\",\"answer\":\"A representation metric such as embedding effective rank can be a transient that later training drives down to a low-rank floor. As a result, the at-grok value can overstate the converged complexity by about 3–5× and may erase qualitative distinctions on the MLP.\"},{\"question\":\"How does the paper distinguish onset time (Tgrok) from compression time (Tcompress)?\",\"answer\":\"It frames the audit to separate generalization onset (when test accuracy rises) from representation compression (when effective rank drops), and it flags censoring and boundary cells that did not fully generalize.\"},{\"question\":\"What controls the lag between generalization onset and representation compression?\",\"answer\":\"A LayerNorm-only one-variable ablation shows the completed fraction of rank compression by the grok step can change substantially, enlarging the post-grok lag. The paper reports that a post-grok separation between onset and compression appears on every architecture tested and varies with the normalization scheme.\"}]","At-Grok Is Not Converged - A Measurement-Validity Audit for Grokking Representation Metrics | PDF",1789978736,66]