[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86438-en":3,"doc-seo-86438-105":30,"detail-sidebar-cat-0-en-105":92},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86438,137441390410,"Hazel","https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984",8,"Research & Report","Interpreting Latent CoT Reasoning as Dynamical Systems","Recent latent reasoning approaches such as CODI and COCONUT face an interpretability challenge: they maintain multiple superimposed candidate reasoning traces in the hidden space at each step, unlike explicit CoT with a single transparent trace. Mechanistic studies reveal compression, shortcuts, and superposition but do not quantify how reasoning evolves across latent steps. This work models latent token sequences as representation-space trajectories and applies dynamical-systems analysis using change, directional consistency, and Lyapunov sensitivity, plus UMAP and DMD/PHATE projections. Results show structured, non-random dynamics with two stability classes: CODI forms a stable attractor while COCONUT behaves as an unstable expanding system; SIM-CoT supervision tightens both behaviors without altering underlying dynamics.","arXiv :2607 .09698v 1 [ cs .AI] 20 Jun 2026  \nICML 2026 Workshop on Foundations of Deep Generative Models: Understanding Memorization, Generalization, and Reasoning  \nInterpreting Latent CoT Reasoning as Dynamical Systems  \nSabari Iyyappan Duraipandian * 1 Shreya Sanjay Boyane * 2 Manju Nagesh 3 Jerome Francis † 4  \nArchana Vaidheeswaran 4 Kevin Zhu 4  \nAbstract  \nRecent latent reasoning methods, such as CODI and COCONUT, face a fundamental interpretability problem: they maintain multiple superimposed candidate traces in the hidden space at each step, unlike explicitCoT, which follows a single transparent reasoning trace. Existing mechanistic methods show compression, shortcuts, and superposition without explaining how reasoning evolves across latent steps. To address this gap, we model latent token sequences as trajectories in representation space and apply dynamical systems analysis to characterize the evolution of reasoning. Using quantitative measures, such as step-to-step change, direction consistency, and Lyapunov sensitivity, alongside qualitative projections, such as UMAP and DMD/PHATE, we show that latent CoT exhibits structured, non-random dynamics with two distinct stability classes. CODI behaves as a stable attractor, while COCONUT behaves as an unstable expanding system, and SIM-CoT supervision tightens both behaviors without changing the underlying dynamics. This framework advances the interpretability of latent CoT reasoning dynamics and provides actionable insights for improving latent reasoning performance. Code 1 and Project page2 available online.  \n1. Introduction  \nLatent CoT paradigms such as CODI and COCONUT have consistently outperformed explicit CoT in the performancecompute tradeoff. However, the interpretability of Latent CoT is still an active area of research. Existing mechanistic interpretation methods (logit lens, attention heatmaps, activation patching) reveal relationships between latent tokens and outputs and the role of latent steps through causality, but do not show how reasoning evolves through latent steps.(Liang & Pan, 2026 ; Goyal et al., 2025) . Prior works demonstrate compression, shortcuts, and superposition in latent CoTs, but do not quantitatively analyze reasoning evolution or highlight quantitative behavior in latent steps.(Liang & Pan, 2026 ; Li et al., 2026) .  \nDynamical systems provide a principled approach to studying how internal representations evolve during reasoning. Applied to explicit CoT, they help evaluate whether models genuinely reason step-by-step or merely memorize (Yu et al., 2025 ; Pham et al., 2026) . These works analyze how often the model shifts and visits different states but do not thoroughly measure the rate, direction, or stability of change—factors crucial for understanding reasoning dynamics. The faithfulness of latent CoT—how much latent steps reflect genuine, step-by-step reasoning rather than opaque computation—remains underexplored and lacks rigorous verification. Dynamical systems offer tools to address this gap. To address this gap, we model latent CoT trajectories as dynamical systems and analyze their stability and representational geometry. Using quantitative metrics and qualitative projections, we investigate whether latent reasoning exhibits structured dynamics and how these dynamics differ across training paradigms.  \n1 San Jose State University. 2Worcester Polytechnic Institute. 3 George Mason University. 4Algoverse AI Research.  \n*Equal contribution; order decided by random coin flip. †Project Lead.  \nCorresponding author: Jerome Francis \u003C[jerome@algoverseairesearch.org](jerome@algoverseairesearch.org)>.  \n1 Code Repository: [https://github.com/SabariIyyappan/Latent-CoT-Reasoning-as-Dynamical-Systems](https://github.com/SabariIyyappan/Latent-CoT-Reasoning-as-Dynamical-Systems)  \n2 Project Page: [https://sabariiyyappan.github.io/Latent-CoT/](https://sabariiyyappan.github.io/Latent-CoT/)  \nAccepted to FoGen 2026: Foundations of Deep Generati","cbCaifj5ccSrIoEm","https://ap.wps.com/l/cbCaifj5ccSrIoEm","pdf",9630802,6,1,15,"English","en",105,"# Abstract\n# Introduction\n# Related Works\n## Chain-of-Thought and Latent Reasoning\n## Mechanistic Interpretability of Latent CoT","[{\"question\":\"What interpretability problem motivates modeling latent CoT as dynamical systems?\",\"answer\":\"Latent CoT keeps multiple superimposed candidate traces in hidden space at each step, unlike explicit CoT’s single trace. Prior mechanistic work explains some structure but does not quantify how reasoning evolves across latent steps.\"},{\"question\":\"How does the proposed method characterize latent reasoning dynamics?\",\"answer\":\"Latent token sequences are treated as trajectories in representation space. Step-to-step change, direction consistency, and Lyapunov sensitivity are used quantitatively, with UMAP and DMD/PHATE projections for qualitative structure.\"},{\"question\":\"What stability behaviors are observed for CODI and COCONUT?\",\"answer\":\"CODI exhibits structured dynamics with a stable attractor behavior, while COCONUT behaves as an unstable expanding system. SIM-CoT supervision tightens both behaviors without changing the underlying dynamics.\"}]",1784211744,38,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"interpreting-latent-cot-reasoning-as-dynamical-systems","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/interpreting-latent-cot-reasoning-as-dynamical-systems/86438/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What interpretability problem motivates modeling latent CoT as dynamical systems?","Question",{"text":76,"@type":77},"Latent CoT keeps multiple superimposed candidate traces in hidden space at each step, unlike explicit CoT’s single trace. Prior mechanistic work explains some structure but does not quantify how reasoning evolves across latent steps.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the proposed method characterize latent reasoning dynamics?",{"text":81,"@type":77},"Latent token sequences are treated as trajectories in representation space. Step-to-step change, direction consistency, and Lyapunov sensitivity are used quantitatively, with UMAP and DMD/PHATE projections for qualitative structure.",{"name":83,"@type":74,"acceptedAnswer":84},"What stability behaviors are observed for CODI and COCONUT?",{"text":85,"@type":77},"CODI exhibits structured dynamics with a stable attractor behavior, while COCONUT behaves as an unstable expanding system. 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