[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85265-en":3,"doc-seo-85265-105":29,"detail-sidebar-cat-0-en-105":91},{"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":20,"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},85265,1374391974585,"Genevieve","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Infrared Organization and Critical Cognitive Field Formation in Transformer Dynamics","Large language models show emergent behaviors, but the mechanism behind their large-scale collective dynamics remains unclear. Cognitive Field Theory links learning to infrared accumulation of slow relaxation modes, reshaping the time-scale density of states and producing a renormalized memory self-energy that reduces the cognitive forgetting gap, thereby enhancing collective susceptibility and forming a macroscopic cognitive field. This work tests these predictions directly in Transformer dynamics using Pythia models, extracting relaxation spectra from layer Jacobians across training and scales.","arXiv :2607 . 10923v 1 [ cs .LG] 12 Jul 2026  \nInfrared Organization and Critical Cognitive Field Formation in Transformer  \nDynamics  \nByung Gyu Chae 1  \n1 Electronics and Telecommunications Research Institute,  \n218 Gajeong-ro, Yuseong-gu, Daejeon 34129, Republic of Korea  \n[bgchae@etri.re.kr](bgchae@etri.re.kr)  \nLarge language models exhibit remarkable emergent behaviors, yet the physical mechanism governing their large-scale collective dynamics remains poorly understood. Cognitive Field Theory predicts that learning reorganizes the time-scale density of states (TDOS) through the infrared accumulation of slow relaxation modes. The resulting memory self-energy renormalizes the cognitive forgetting gap,  \nrcog = r − Σ(0),  \nwhere r denotes the bare forgetting rate and Σ(0) is the memory self-energy. As the forgetting gap decreases, the collective susceptibility  \nχ(0) ∝ r−co1g  \nis strongly enhanced, signaling the formation of a macroscopic cognitive field.  \nIn the present work, we investigate whether these collective observables can be identified directly in Transformer dynamics. Using publicly available Pythia language models, we extract relaxation spectra from layer Jacobians throughout training, network depth, and model scale, allowing the TDOS, memory self-energy, forgetting gap, memory kernel, and infrared critical exponent to be measured quantitatively.  \nThe measurements reveal a pronounced infrared reorganization of the relaxation spectrum. Across all investigated models, slow relaxation modes progressively accumulate toward the infrared sector, producing an approximately flat infrared TDOS consistent with  \nρ (λ) ∼ λβ , β ≃ −0 .1 ,  \nwhile the corresponding memory kernels exhibit a robust universal long-memory scaling,  \n1 K (t) ∼  \nt .  \nA central experimental observation is that the memory self-energy does not increase monotonically during optimization. Instead, it exhibits a pronounced transient maximum during the early stage of learning before relaxing toward a finite metastable near-critical regime. Within Cognitive Field Theory, this transient maximum corresponds to the smallest cognitive forgetting gap and therefore to the largest collective susceptibility, indicating a transient critical formation of the cognitive field.  \nThe measured evolution of the TDOS, memory self-energy, cognitive forgetting gap, collective susceptibility, and scale-free memory kernel is consistent with the central predictions of Cognitive Field Theory. Together, these observations demonstrate that infrared spectral reorganization progressively enhances the memory self-energy, renormalizes the cognitive forgetting gap, and strengthens the collective susceptibility, providing quantitative experimental evidence that Transformer learning is governed by infrared collective organization. The reproducibility of the same dynamical scenario across training, network depth, and Transformer model scales, together with the depth-independent 1/t memory kernel, suggests that infrared slow-mode organization constitutes a universal collective principle underlying Transformer dynamics.  \nI. INTRODUCTION  \nLarge language models based on the Transformer architecture have demonstrated remarkable emergent capabilities, including reasoning, abstraction, in-context learning, and long-range contextual memory [1–5] . Despite these advances, the physical mechanism governing their large-scale collective organization remains largely unknown. Most existing studies describe Transformer computation as a high-dimensional nonlinear mapping or an attention-based optimization process [6–11] . While these viewpoints successfully characterize information  \nprocessing, they provide limited insight into how largescale collective organization arises from the underlying Transformer dynamics.  \nFrom the perspective of statistical physics, macroscopic collective behavior is governed not only by microscopic interactions but also by the organization of collective dynamical mod","cbCaimUNzVBlsRQw","https://ap.wps.com/l/cbCaimUNzVBlsRQw","pdf",8916756,1,37,"English","en",105,"# Introduction\n## Cognitive Field Theory and Collective Observables\n## Objective and Methodology","[{\"question\":\"What does Cognitive Field Theory predict about learning in Transformers?\",\"answer\":\"It predicts that learning reorganizes the time-scale density of states through infrared accumulation of slow relaxation modes, renormalizing memory self-energy and reducing the cognitive forgetting gap to enhance collective susceptibility.\"},{\"question\":\"How are the collective observables measured in this study?\",\"answer\":\"The approach uses publicly available Pythia language models and extracts relaxation spectra from layer Jacobians during training, across depth and model scale, enabling quantitative measurement of TDOS, memory self-energy, forgetting gap, memory kernel, and an infrared critical exponent.\"},{\"question\":\"What key experimental findings appear in the infrared regime?\",\"answer\":\"Relaxation modes accumulate toward the infrared sector, yielding an approximately flat infrared TDOS and universal long-memory scaling in memory kernels. The memory self-energy shows a transient early maximum and relaxes toward a metastable near-critical regime.\"}]",1784202161,93,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":27},"infrared-organization-and-critical-cognitive-field-formation-in-transformer-dynamics","",{"@graph":35,"@context":85},[36,53,68],{"@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/infrared-organization-and-critical-cognitive-field-formation-in-transformer-dynamics/85265/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What does Cognitive Field Theory predict about learning in Transformers?","Question",{"text":75,"@type":76},"It predicts that learning reorganizes the time-scale density of states through infrared accumulation of slow relaxation modes, renormalizing memory self-energy and reducing the cognitive forgetting gap to enhance collective susceptibility.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are the collective observables measured in this study?",{"text":80,"@type":76},"The approach uses publicly available Pythia language models and extracts relaxation spectra from layer Jacobians during training, across depth and model scale, enabling quantitative measurement of TDOS, memory self-energy, forgetting gap, memory kernel, and an infrared critical exponent.",{"name":82,"@type":73,"acceptedAnswer":83},"What key experimental findings appear in the infrared regime?",{"text":84,"@type":76},"Relaxation modes accumulate toward the infrared sector, yielding an approximately flat infrared TDOS and universal long-memory scaling in memory kernels. The memory self-energy shows a transient early maximum and relaxes toward a metastable near-critical regime.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]