[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81973-en":3,"doc-seo-81973-105":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},81973,1099514068035,"Ezra","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Computing with Stochastic Oracles in AI-Augmented Computation","The Stochastic-Oracle Turing Machine (SOTM) framework formalizes AI-augmented computation as a probabilistic Turing machine interacting with a context-dependent stochastic oracle via queries and responses. The paper analyzes two response schemes—cached responses with reuse versus fresh responses with independent resampling—under adaptive query generation from a transcript. Cached responses create transcript-based ceilings for identification accuracy and attainable output quality, while fresh responses can lift them through repeated evidence accumulation, including exponential Chernoff error gains in a binary single-query setting.","arXiv :2607 .06893v 1 [ cs .CC] 8 Jul 2026  \nComputing with Stochastic Oracles in AI-Augmented  \nComputation  \nJie Wang ∗  \n[Jie_Wang@uml.edu](Jie_Wang@uml.edu)  \nAbstract  \nThe Stochastic-Oracle Turing Machine (SOTM) framework models AI-augmented computation as the interaction of a probabilistic Turing machine with an oracle whose responses are drawn from context-dependent distributions. This paper studies what an SOTM can achieve under two oracle-response schemes: in a cached-response oracle, each distinct query receives one response that is reused on later calls to the same query, while in a fresh-response oracle, each call returns an independent response. In both schemes, the SOTM first computes from its input and internal random source to generate its first query, then proceeds adaptively, computing from its query-response transcript (the record of queries issued and responses received) to generate each subsequent query or produce a final output. Cached responses impose two transcript-based ceilings on achievable performance: a correct-identification ceiling governed by the total variation distance between the transcript distributions induced by the hidden states of the oracle, and an output quality ceiling equal to the expected score of the best output the SOTM can compute from the transcript. Fresh responses can raise these ceilings by allowing repeated calls to accumulate independent evidence toward correct or high-quality outputs. In the binary single-informative-query case, the error probability decreases exponentially in the number of calls to the same query at the Chernoff rate. For output quality, query-count bounds characterize threshold stopping when the score function is incorporated as part of the SOTM, and majority-based amplification bounds characterize the binary candidate-output model when it is not. Together, the results identify how response reuse, transcript information, and access to the score function determine what an SOTM can compute and at what token cost.  \n1 Introduction  \nAI-augmented computing delegates knowledge-intensive or skill-intensive subtasks to stochastic systems. A program may ask a general-purpose large language model (LLM), a domain-specific finetuned model, or more generally a family of AI systems with a built-in control mechanism, to solve a problem instance, produce code, or judge a candidate solution, among other tasks. Wang [4] introduced the Stochastic-Oracle Turing Machine (SOTM) framework 1 to formalize this paradigm, in which a probabilistic Turing machine interacts with a stochastic oracle through a query-response interface, with responses drawn from query-dependent distributions. Wang also introduced token complexity as an exact measure of the token cost for solving a given task at a given quality level:  \n∗ Richard A. Miner School of Computing and Information Sciences, University of Massachusetts, Lowell, MA 01854, USA.  \n1Wang originally called the model the AI-Oracle Turing Machine (AOTM) [4], and later renamed it the StochasticOracle Turing Machine [5] . The term “AI” is context-dependent, while “stochastic” names the mathematically defined feature of the oracle.  \nthe minimum expected weighted sum of query and response tokens, with query-token weight α > 0 and response-token weight β > 0. In what follows,“stochastic oracle” is abbreviated as “oracle.”  \nIn practice, a system engineer may choose an LLM with strong benchmark performance as an oracle and build a system to interact with it for completing a given task. Benchmark performance alone, however, may not reveal the response distributions that matter on the task instances at hand. Even if those distributions are known or approximately modeled, one may still want to know what an adaptive SOTM can achieve from interacting with the chosen oracle to inform the design of the system. This paper studies that question under two oracle-response schemes. Under cached responses, each distinct query receives one response tha","cbCaiefnCNadSnVt","https://ap.wps.com/l/cbCaiefnCNadSnVt","pdf",525259,6,1,18,"English","en",105,"# Abstract\n# Introduction\n## Stochastic-Oracle Turing Machine (SOTM) framework\n## Cached vs fresh oracle responses\n## Transcript-based identification and output-quality ceilings","[{\"question\":\"What is the Stochastic-Oracle Turing Machine (SOTM) framework?\",\"answer\":\"SOTM models AI-augmented computation as a probabilistic Turing machine that issues queries to a stochastic oracle and receives responses drawn from query-dependent, context-dependent distributions.\"},{\"question\":\"How do cached responses and fresh responses differ in the SOTM setting?\",\"answer\":\"In a cached-response oracle, each distinct query gets one response that is reused for later calls; in a fresh-response oracle, repeated calls to the same query return independent samples.\"},{\"question\":\"Why do cached responses impose transcript-based ceilings on performance?\",\"answer\":\"Because reusing the same response on repeated queries prevents the transcript from accumulating new evidence, limiting both identification accuracy (via total variation distance between transcript distributions) and output quality (via the expected score of the best computable output from the transcript).\"}]",1784177360,45,{"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},"computing-with-stochastic-oracles-in-ai-augmented-computation","",{"@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/computing-with-stochastic-oracles-in-ai-augmented-computation/81973/",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","2026-07-30","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 is the Stochastic-Oracle Turing Machine (SOTM) framework?","Question",{"text":76,"@type":77},"SOTM models AI-augmented computation as a probabilistic Turing machine that issues queries to a stochastic oracle and receives responses drawn from query-dependent, context-dependent distributions.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How do cached responses and fresh responses differ in the SOTM setting?",{"text":81,"@type":77},"In a cached-response oracle, each distinct query gets one response that is reused for later calls; in a fresh-response oracle, repeated calls to the same query return independent samples.",{"name":83,"@type":74,"acceptedAnswer":84},"Why do cached responses impose transcript-based ceilings on performance?",{"text":85,"@type":77},"Because reusing the same response on repeated queries prevents the transcript from accumulating new evidence, limiting both identification accuracy (via total variation distance between transcript distributions) and output quality (via the expected score of the best computable output from the transcript).","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,111,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},"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":107,"slug":138},19,"General","general"]