[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85304-en":3,"doc-seo-85304-105":30,"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":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},85304,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","Valid Necessary: Diagnosing Latent Inefficiency in Chain-of-Thought","Chain-of-Thought (CoT) prompting improves large language model reasoning but often triggers substantial computational overhead through “over-reasoning,” including redundant, verbose, or irrelevant steps. Existing evaluators detect logical or factual faults yet miss a key case: “valid but inefficient” steps that inflate token usage without advancing the solution. RIV-GSM8K introduces five inefficiency types to diagnose this blind spot. CAID (Context-Aware Information Density) distills low-utility steps without training, and PACE compression achieves 31–53% token savings on GSM8K, StrategyQA, and ARC-Challenge while preserving accuracy.","Valid  Necessary: Diagnosing Latent Inefficiency in Chain-of-Thought  \nDaeyeop Lee 1 ,2 and Hwanjo Yu2 *  \n1 KT Corporation  \n2Pohang University of Science and Technology  \n[daeyeop.lee@kt.com](daeyeop.lee@kt.com)  \n[hwanjoyu@postech.ac.kr](hwanjoyu@postech.ac.kr)  \narXiv :2607 . 1 1266v 1 [ cs .AI] 13 Jul 2026  \nAbstract  \nChain-of-Thought (CoT) prompting has significantly advanced the reasoning capabilities of Large Language Models (LLMs), yet it often incurs substantial computational costs due to“over-reasoning”—the generation of redundant, verbose, or irrelevant steps. While existing reasoning step evaluators effectively detect logical fallacies and factual errors, our analysis reveals a critical blind spot: they fail to penalize “valid but inefficient” reasoning steps that inflate token usage without contributing to the solution. To systematically diagnose this limitation, we introduce RIV-GSM8K, a diagnostic benchmark injected with five distinct types of inefficiencies, including circular reasoning and excessive decomposition. Diagnostic experiments reveal that state-of-the-artevaluators struggle to distinguish these inefficiencies from necessary reasoning. To address this gap, we propose CAID (Context-Aware Information Density), a training-free metric grounded in information theory that identifies low-utility steps. To validate the metric’s practical utility, we apply it within PACE, a post-hoc compression strategy. Additional control experiments show that the gains of PACE are not explained by trivial pruning: compared with random step removal and PRM-based compression baselines, it preserves accuracy at substantially higher compression rates. Empirical resultson GSM8K, StrategyQA, and ARC-Challenge demonstrate that PACE reduces token consumption by 31–53% while maintaining accuracy, confirming that CAID successfully distills informational “froth” from reasoning chains without compromising deductive validity.  \n1 Introduction  \nLarge Language Models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks, largely driven by the Chain-of-Thought (CoT) prompting strategy (Wei et al., 2022) . By  \n* Corresponding author.  \n\n|  | Augmented Reasoning Chain |\n| --- | --- |\n| Simple Duplication | [Step 1] [Step 2] [Step 2] [Step 3]\u003Cbr>Repeats an existing step exactly. |\n| Paraphrase | [Step 1] [Step 2]  Rephrased [Step 2] \u003Cbr> [Step 3]\u003Cbr>Inserts a step with an equivalent expression. |\n| Circular Reasoning |  |\n|  | Add steps that loop back to the same information. |\n| Decompose |  [Step 1]  [Step 2a]  [Step 2b]  ··· \u003Cbr>Breaks down a single step into smaller, verbose sub-steps.\u003Cbr>\u003Cbr>[Step 3] |\n| Irrelevant | [Step 1] [Step 2] [Irrelevant Fact] [Step 3]\u003Cbr>Inserts contextually related but non-contributory steps. |\n\nLegend:  Original Step,  Augmented/Modified Step,  Flow of Reasoning  \nFigure 1: Taxonomy of reasoning inefficiencies in RIVGSM8K. The diagram illustrates how five distinct types of redundant steps are synthetically injected into the reasoning chain to simulate valid but dispensable “froth.”  \ndecomposing complex problems into intermediate steps, CoT helps bridge the gap between question and answer. However, these gains often come at the cost of inference efficiency. Recent studies show that LLMs tend to “over-reason” by generating verbose explanations, repetitive statements, or contextually irrelevant details that increase computational cost without adding deductive value (Turpin et al., 2023 ; Wang et al., 2023 ; Chiang and Lee, 2024) . More recent work has therefore begun to treat reasoning efficiency itself as an important objective, for example through rationale reduction and concise intermediate reasoning formats (Janget al., 2025 ; Xu et al., 2025) .  \nTo assess and improve reasoning quality, various Process Reward Models (PRMs) and reasoningstep evaluators have been proposed, including ReasonEval and Math-Shepherd (Xia et al., 2025 ; Wang et al., 2024) . More broadly, recent benchmarks ","cbCaioriZgyyTMRF","https://ap.wps.com/l/cbCaioriZgyyTMRF","pdf",776268,4,1,17,"English","en",105,"# Abstract\n# Introduction\n## CoT prompting and over-reasoning\n## Limits of step evaluators\n## RIV-GSM8K benchmark\n## CAID metric and PACE compression","[{\"question\":\"What problem does the paper identify in existing Chain-of-Thought evaluation?\",\"answer\":\"The paper shows that current step evaluators mainly reward correctness and logical validity, but often fail to penalize “valid but inefficient” steps that increase token usage without contributing to the final solution.\"},{\"question\":\"How does RIV-GSM8K diagnose latent reasoning inefficiency?\",\"answer\":\"RIV-GSM8K injects five distinct inefficiency types into GSM8K-derived reasoning chains, including duplication, paraphrase, circular reasoning, decomposition, and irrelevant steps, to test whether evaluators can distinguish necessary from dispensable reasoning.\"},{\"question\":\"What are CAID and PACE, and how do they improve efficiency?\",\"answer\":\"CAID is a training-free metric based on information theory that identifies low-utility reasoning steps using signals such as novelty and goal alignment. PACE applies this metric for post-hoc compression, reducing tokens by 31–53% on GSM8K, StrategyQA, and ARC-Challenge while maintaining accuracy.\"}]",1784202352,43,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":28},"valid-necessary-diagnosing-latent-inefficiency-in-chain-of-thought","",{"@graph":36,"@context":85},[37,53,68],{"@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":20},"https://docshare.wps.com/document/valid-necessary-diagnosing-latent-inefficiency-in-chain-of-thought/85304/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-23","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 problem does the paper identify in existing Chain-of-Thought evaluation?","Question",{"text":75,"@type":76},"The paper shows that current step evaluators mainly reward correctness and logical validity, but often fail to penalize “valid but inefficient” steps that increase token usage without contributing to the final solution.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does RIV-GSM8K diagnose latent reasoning inefficiency?",{"text":80,"@type":76},"RIV-GSM8K injects five distinct inefficiency types into GSM8K-derived reasoning chains, including duplication, paraphrase, circular reasoning, decomposition, and irrelevant steps, to test whether evaluators can distinguish necessary from dispensable reasoning.",{"name":82,"@type":73,"acceptedAnswer":83},"What are CAID and PACE, and how do they improve efficiency?",{"text":84,"@type":76},"CAID is a training-free metric based on information theory that identifies low-utility reasoning steps using signals such as novelty and goal alignment. PACE applies this metric for post-hoc compression, reducing tokens by 31–53% on GSM8K, StrategyQA, and ARC-Challenge while maintaining accuracy.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]