[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-273418-105":59,"doc-detail-273418-en":123},{"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":116,"head_meta":118,"extra_data":120,"updated_unix":122},105,"en","what-iterated-self-feeding-probes-of-language-models-measure-and-a-test-that-separates-the-construction-from-the-model","What Iterated Self-Feeding Probes of Language Models Measure - and a test that separates the construction from the model","","A growing family of methods probes language models by repeatedly feeding them their own outputs, including self-consistency, iterated refinement, and agentic loops. The study asks what such probes measure, using a sharp construction based on resampling a ring of token cells in place via the model’s windowed conditional distribution. Glauber-dynamics substrate with common-random-number coupling makes damage spreading observable, revealing that the probe measures both probe-specific and model-specific quantities. A validated discriminator distinguishes them via controlled factor variations and reports estimator failures.",{"@graph":69,"@context":115},[70,84,106],{"@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/what-iterated-self-feeding-probes-of-language-models-measure-and-a-test-that-separates-the-construction-from-the-model/273418/",{"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/what-iterated-self-feeding-probes-of-language-models-measure-and-a-test-that-separates-the-construction-from-the-model/273418.png","ImageObject",300,407,{"name":92,"@type":93},"Finn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109],{"name":110,"@type":111,"acceptedAnswer":112},"How does the paper separate probe-specific effects from model-specific effects?","Question",{"text":113,"@type":114},"It introduces a test that varies one factor while holding the other fixed, checking which readings move under changes to the construction versus changes to the model (and training checkpoint).","Answer","https://schema.org",{"og:url":83,"og:type":117,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":119,"canonical":83},"index,follow",{"doc_id":121,"site_id":62},273418,1789471326,{"code":4,"msg":5,"data":124},{"doc_id":121,"user_id":125,"nickname":92,"user_avatar":126,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":127,"file_id":128,"file_url":129,"file_type":130,"file_size":131,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":132,"language":133,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":134,"faqs":135,"seo_title":136,"seo_description":67,"update_tm":122,"read_time":36,"preview_page_count":4},34359740700684,"https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487","arXiv :2608 . 10986v1 [ cs .CL] 11 Aug 2026  \nWhat Iterated Self-Feeding Probes of Language Models Measure  \nand a test that separates the construction from the model  \nNicolás Vera Zúñiga  \nIndependent Researcher, Chile  \n[nicovera@quetru. cl](nicovera@quetru. cl)  \nAbstract  \nA growing class of methods probes a language model by feeding it its own output: selfconsistency, iterated refinement, agentic loops. We ask what such a probe measures, in a construction chosen to make the question sharp: a ring of token cells resampled in place by the model’s own windowed conditional pr (xi | xi±r) . The substrate is Glauber dynamics ontoken sequences and is not new; what we change is the coupling. Advancing two rings that differ in one token under common random numbers makes undamaged copies diverge by exactly zero, so damage spreading becomes measurable where a maximal coupling gives mixing times instead. The answer is that it measures two different things at once, in readings that look alike. Some quantities are fixed by the construction: the damage light cone is kinematic, and the radius scaling of the token-space Lyapunov exponent λca (r) is model-invariant across 19 models and two scale ladders spanning 70 × . Others genuinely track the model: λca crosses zero at a reproducible point in training, and the attractor share ranks models consistently however the lattice is built. Left undistinguished, the first kind is readily mistaken for the second—we did so ourselves for four months, and report a phase transition we measured to three decimal places that belongs to the probe rather than to any language model. We give the test that separates them: hold the construction fixed and vary the model, or hold the model fixed and vary the construction, and see which readings move. We validate the instrument by reproduction first, recovering a Domany–Kinzel damage field bit-exactly against an independent prediction, and we report the estimator failures that this discipline caught—four retracted verdicts, each on a quantity that looked like a measurement. The methodology ships as a package.  \n1 Introduction  \nFeeding a language model its own output is now routine. Self-consistency samples a model repeatedly and aggregates [Wang et al. , 2022], on reasoning traces the model produced itself [Wei et al. , 2022]; iterated refinement asks a model to revise its own answer against its own critique [Madaan et al. , 2023]; agentic loops return a model’s output to its input for many turns. Each of these is a dynamical system built from a static predictor, and each invites a natural question: what do the dynamics tellus about the model?  \nThis paper answers a prior question, because we found it has an unobvious answer. Before asking what an iterated probe reveals, one must ask what it measures —and the answer is that it measures the model and the probe together, in quantities that are not distinguishable by inspection.  \nWe work in a construction chosen to make the confound as stark as possible: a ring of N token cells, each resampled in place from the model’s own windowed conditional pr(xi | xi±r) at temperature T , so that the model’s output at every site is part of its own input at the next step and no external text enters after initialisation.  \nThe substrate is not new, and we do not claim it. In-place resampling of masked tokens is Glauber dynamics on token sequences, and it has been studied as such [Sana et al. , 2026] . What we change is the coupling and therefore the observable. That work couples two chains maximally and measures mixing time and metastability—how long the chain takes to forget where it started. We couple with common random numbers: two rings, identical but for one flipped token, advanced with the same stream of uniform variates and the same visit order. Maximal coupling and CRN coupling are provably distinct constructions, and they answer different questions. Under CRN, two rings whose windows agree draw the same token, so undam","cbCaivwDgULui7Z1","https://ap.wps.com/l/cbCaivwDgULui7Z1","pdf",866511,16,"English","# Abstract\n# Introduction\n## Construction and coupling setup\n## Contributions\n# Discriminator and estimator gating","[{\"question\":\"How does the paper separate probe-specific effects from model-specific effects?\",\"answer\":\"It introduces a test that varies one factor while holding the other fixed, checking which readings move under changes to the construction versus changes to the model (and training checkpoint).\"}]","What Iterated Self-Feeding Probes of Language Models Measure - and a test that separates the construction from the model | PDF"]