[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82754-en":3,"doc-seo-82754-105":30,"detail-sidebar-cat-0-en-105":83},{"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},82754,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","Differentiate the Evaluator, Not the Program: An Efficient Runtime Representation for Neuro-Symbolic Learning","AI systems increasingly propose executable scientific models, yet their value depends on both symbolic/mechanistic structure and continuous parameters calibrated against observations. This creates a co-search bottleneck: thousands of candidate programs from an outer loop each require costly inner optimization before evaluation. Existing approaches trade off program-as-data search flexibility against interpreter or tracing overhead. NDVM separates native symbolic runtime structure from batched numeric state with recorded reverse-mode gradients, enabling amortized evaluator walks, faster calibration, and preserved first-class program candidates.","arXiv :2607 .03574v 1 [ cs .LG] 3 Jul 2026  \nDIFFERENTIATE THE EVALUATOR, NOT THE PROGRAM: AN EFFICIENT RUNTIME REPRESENTATION FOR NEURO-SYMBOLIC LEARNING  \nA PREPRINT  \nLucas Sheneman  \nInstitute for Interdisciplinary Data Sciences  \nUniversity of Idaho  \n[sheneman@uidaho.edu](sheneman@uidaho.edu)  \nJuly 7, 2026  \nABSTRACT  \nAI systems are beginning to propose executable scientific models whose value depends not only on their symbolic or mechanistic structure, but also on the continuous parameters that must be calibrated against observations. This creates a central bottleneck for scientific co-search: an outer loop can generate thousands of candidate model programs, but each candidate may require an expensive inner optimization before its scientific promise can be assessed. The challenge is especially acute for models that combine interpretable mechanistic structure with rich quantitative parameterization, where both the form of the model and its fitted constants matter.  \nExisting implementation strategies force an undesirable tradeoff. Staging each candidate program into its own differentiable graph can make individual models fast, but sacrifices the program-asdata property needed for fluid search over many structurally distinct candidates. Interpreter-based approaches preserve programs as runtime data, but the cost of representing and walking the interpreter can dominate the actual numerical work. As a result, parameter calibration becomes the limiting factor in co-search rather than model generation or scientific evaluation.  \nWe present the Native Differentiable Virtual Machine (NDVM), an efficient runtime representation for differentiating executable programs without compiling each candidate into a separate graph. NDVM separates symbolic structure from differentiable numeric state: tags, symbols, environments, and control remain native runtime data, while numeric payloads live in dense batched buffers with exact reverse-mode gradients recorded along the realized execution trace. This allows one evaluator walk to be amortized across large populations of parameter vectors, enabling efficient gradient-based calibration while preserving programs as first-class search objects.  \nA locked cost model of a real differentiable self-hosted Scheme interpreter motivates the design, showing that execution is dominated by interpreter representation and traversal rather than arithmetic. We realize NDVM as a native runtime and demonstrate forward and gradient equivalence to the baseline backend across a diverse program suite, including matrix-valued Kalman filter models. NDVM reduces per-lane calibration cost by approximately 60 × through batch amortization, scales nearlinearly across CPU cores, and generalizes across multiple front ends, including both a differentiable Scheme interpreter and a differentiable stack-bytecode virtual machine.  \nIn fixed-budget co-search experiments over LLM-proposed programs, NDVM reaches high-quality solutions approximately 24 × sooner in wall-clock time and enables substantially deeper exploration of candidate model space. These results suggest that efficient runtime differentiation can make parameter calibration fast enough to keep pace with AI-generated model proposals, providing a practical systems foundation for scientific discovery workflows that jointly search over mechanistic structure and quantitative parameterization.  \n1 Introduction  \nA growing body of work differentiates through the execution of a program rather than through a single static numeric graph. Program-and-parameter co-search calibrates the continuous constants of machine-proposed programs against data (Sheneman, 2026; Novikov et al., 2025; Romera-Paredes et al., 2024); neurosymbolic methods learn through discrete program structure (Chaudhuri et al., 2021; Manhaeve et al., 2018; Li et al., 2023); and differentiable interpreters make program behavior trainable (Gaunt et al., 2016; Bošnjak et al., 2017; Feser et al., 2016; Macfarla","cbCainkHvYqLj1lg","https://ap.wps.com/l/cbCainkHvYqLj1lg","pdf",622239,2,1,30,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"How does the locked cost model motivate NDVM’s design?\",\"answer\":\"The paper uses a locked, reproducible cost model of a differentiable self-hosted Scheme interpreter to show execution is dominated by interpreter representation and traversal, not arithmetic. This motivates optimizing representational overhead in runtime differentiation.\"}]",1784182709,76,{"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":78,"head_meta":80,"extra_data":82,"updated_unix":28},"differentiate-the-evaluator-not-the-program-an-efficient-runtime-representation-for-neuro-symbolic-learning","",{"@graph":36,"@context":77},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/differentiate-the-evaluator-not-the-program-an-efficient-runtime-representation-for-neuro-symbolic-learning/82754/",4,{"url":51,"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","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"How does the locked cost model motivate NDVM’s design?","Question",{"text":75,"@type":76},"The paper uses a locked, reproducible cost model of a differentiable self-hosted Scheme interpreter to show execution is dominated by interpreter representation and traversal, not arithmetic. This motivates optimizing representational overhead in runtime differentiation.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,114,119,122,126],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":22,"slug":113},"research-report",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":98,"slug":129},19,"General","general"]