[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-273658-105":59,"doc-detail-273658-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","forking-fast-efficiently-estimating-uncertainty-dynamics-in-text-generation","Forking Fast - Efficiently Estimating Uncertainty Dynamics in Text Generation","","LLM reasoning is stochastic, so understanding a model requires characterizing the distribution of reasoning chains and the resulting uncertainty over final answers. Resampling-based analyses reveal which rollout steps drive this uncertainty, but resampling at every token or sentence is prohibitively costly. This work develops a computationally efficient statistical model for uncertainty dynamics and uses it to smooth noisy, low-sample resampling estimates toward high-sample behavior in text generation.",{"@graph":69,"@context":123},[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/forking-fast-efficiently-estimating-uncertainty-dynamics-in-text-generation/273658/",{"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/forking-fast-efficiently-estimating-uncertainty-dynamics-in-text-generation/273658.png","ImageObject",300,407,{"name":92,"@type":93},"Riley","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"Why is uncertainty in LLM reasoning difficult to analyze directly?","Question",{"text":113,"@type":114},"LLM reasoning is stochastic, producing many possible reasoning chains for a given question. Uncertainty depends on the distribution of these rollouts and which steps change the likelihood of different final answers.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What limitation affects existing resampling-based uncertainty analyses?",{"text":118,"@type":114},"Resampling every token or sentence in a reasoning chain is computationally very expensive. It often requires millions of tokens to analyze a single reasoning chain.",{"name":120,"@type":111,"acceptedAnswer":121},"How does the proposed approach reduce computation while improving uncertainty estimation?",{"text":122,"@type":114},"It develops a statistical model to smooth noisy low-sample rollout data to better approximate high-sample results. By using change point detection and kernel-pooling, it recovers stable uncertainty dynamics and sharp forking points with much lower sampling costs.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},273658,1789472398,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":105,"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":130,"read_time":144,"preview_page_count":4},1374391975076,"https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051","Forking Fast: Efficiently Estimating Uncertainty Dynamics in Text Generation  \nEric Bigelow, Amir Zur, Satchel Grant, Tal Haklay, Can Rager, Owen Lewis, Thomas McGrath, Jack Merullo, Ekdeep Singh Lubana, Atticus Geiger  \narXiv : 2608 . 196 1 1v 1 [cs .CL] 20 Aug 2026  \nAbstract  \nLLM reasoning is stochastic, and so understanding a model requires grappling with the distribution of reasoning chains that it might produce for a given question, i.e., its uncertainty. Resampling-based analyses characterize this distribution, revealing which steps of a rollout determine how the model arrives at its answer. However, a major limitation of these approaches is that resampling text sequences at every token or sentence in a reasoning chain is very costly. Our work strives to make resampling analysis more computationally efficient, while also shedding light on an important scientific question: what is the right statistical model for explaining uncertainty dynamics in text generation? We show that when resampling many reasoning chains, uncertainty dynamics converge to stable patterns, and noise is largely an artifact of sampling rather than an LLM’s sensitivity to each individual token or reasoning step. We develop a statistical model for smoothing noisy low-sample rollout data to better approximate high-sample data, allowing us to significantly cut sampling costs.  \n1 Introduction  \nWhen Large Language Models (LLMs) engage in long-form text generation such as reasoning, there are many possible paths they might take at each step or token that they generate. Prior work has shown that specific steps during reasoning can have a significant impact on the model’s overall behavior, while many other steps are not as important (Bigelow et al., 2024a ; Bogdan et al., 2025 ; Zhang et al., 2025 ; Macar et al., 2026 ; Boppana et al., 2026) . One method for understanding which steps of reasoning (and text generation more generally) are most important is resampling: given a single reasoning rollout, resample alternate rollouts at  \nCode and interactive dashboard: [https://github.com/](https://github.com/)[ ](https://github.com/)[ericb-goodfire/forking-fast](ericb-goodfire/forking-fast)  \neach step of reasoning, then collect the final answers of all rollouts and aggregate them into a distribution.  \nResampling methods such as Forking Paths Analysis (FPA) (Bigelow et al., 2024a) can provide critical insight into uncertainty dynamics in text generation, where uncertainty measures how likely an LLM is to pick one answer over another. However, this approach is very costly and often requires millions of tokens to analyze a single reasoning chain. In this work, we propose a more efficient way to approximate these uncertainty dynamics by developing a statistical model of their distribution, and using this model to smooth noisy low-sample estimates.  \nWe evaluate our approach by studying Chainof-Thought reasoning (Kojima et al., 2022) in Llama-3-8B-Instruct (Grattafiori et al., 2024) and the native reasoning model DeepSeek-R1-DistillLlama-8B (DeepSeek-AI et al., 2025) as they solve problems in tinyMMLU (Maia Polo et al., 2024 ; Hendrycks et al., 2021) . After collecting and analyzing reasoning data with nearly two billion tokensin total, we find three main results:  \n1. When resampling a small number of times, the uncertainty dynamics of reasoning rollouts are quite noisy (Bigelow et al., 2024a) . However, when resampling hundreds of times, the uncertainty dynamics become increasingly smooth, except at key forking points which have sharp changes. We find that variation across reasoning rollouts is modeled well as multinomial sampling noise (§3.3), and reconstruction error decays in proportion to the square root of the amount of samples collected.  \n2. We develop a statistical model which allows us to approximate high-sample uncertainty dynamics by smoothing lower-sample data. This model uses change point detection to identify forking points, and kernel-pooling to ","cbCaial0ukrbSjNZ","https://ap.wps.com/l/cbCaial0ukrbSjNZ","pdf",645517,"English","# Introduction\n## Forking Paths Analysis and resampling\n## Problem: computational cost and uncertainty modeling\n# Methods\n## Forking Paths Analysis setup\n## Efficient resampling approximations","[{\"question\":\"Why is uncertainty in LLM reasoning difficult to analyze directly?\",\"answer\":\"LLM reasoning is stochastic, producing many possible reasoning chains for a given question. Uncertainty depends on the distribution of these rollouts and which steps change the likelihood of different final answers.\"},{\"question\":\"What limitation affects existing resampling-based uncertainty analyses?\",\"answer\":\"Resampling every token or sentence in a reasoning chain is computationally very expensive. It often requires millions of tokens to analyze a single reasoning chain.\"},{\"question\":\"How does the proposed approach reduce computation while improving uncertainty estimation?\",\"answer\":\"It develops a statistical model to smooth noisy low-sample rollout data to better approximate high-sample results. By using change point detection and kernel-pooling, it recovers stable uncertainty dynamics and sharp forking points with much lower sampling costs.\"}]","Forking Fast - Efficiently Estimating Uncertainty Dynamics in Text Generation | PDF",33]