[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-563814-105":53,"doc-detail-563814-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","cryptol-towards-scale-dominance-and-physics-constraints-mitigation-in-financial-multivariate-time-series-forecasting","CryptoL - Towards Scale Dominance and Physics Constraints Mitigation in Financial Multivariate Time Series Forecasting","","Cryptocurrency forecasting faces extreme cross-asset scale heterogeneity, nonstationary dynamics, and structural dependencies among Open–High–Low–Close (OHLC) variables. CryptoL introduces a unified multivariate time-series framework that evaluates error in context-normalized coordinates within RevIN, avoiding inverse-normalization artifacts that add squared-scale weighting to MSE. It characterizes how large-scale assets can dominate optimization, studies channel-independent versus channel-dependent normalization for order preservation, adds scale-adaptive stabilization for numeric robustness, and introduces a soft feasibility loss to penalize OHLC inequality violations. Experiments on heterogeneous assets with controlled ablations show improved accuracy, training stability, and more financially valid OHLC predictions.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/cryptol-towards-scale-dominance-and-physics-constraints-mitigation-in-financial-multivariate-time-series-forecasting/563814/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/cryptol-towards-scale-dominance-and-physics-constraints-mitigation-in-financial-multivariate-time-series-forecasting/563814.png","ImageObject",442,249,{"name":88,"@type":89},"Aran","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-26","2026-10-12",true,{"@type":98,"interactionType":99,"userInteractionCount":79},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What core problem does CryptoL target in cryptocurrency OHLC forecasting?","Question",{"text":108,"@type":109},"It targets scale dominance and the preservation of physical candlestick structure while handling nonstationary dynamics and cross-asset heterogeneity across OHLC variables.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How does CryptoL modify RevIN to reduce unintended scale weighting in MSE?",{"text":113,"@type":109},"CryptoL evaluates forecasting error in context-normalized coordinates in the RevIN pipeline, preventing inverse normalization from introducing additional squared-scale weighting into the MSE objective.",{"name":115,"@type":106,"acceptedAnswer":116},"Why does CryptoL include a soft feasibility loss for OHLC predictions?",{"text":117,"@type":109},"Because models can still produce financially inadmissible outputs that violate candlestick inequality rules; the auxiliary physics-informed loss penalizes these violations to maintain feasibility.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},563814,1792438124,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":79,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":135,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":141},137455076865,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","CryptoL: Towards Scale Dominance and Physics Constraints Mitigation in Financial Multivariate Time Series Forecasting  \nYalda Taheri 1∗, Mohammad Hassan Heydari2∗, Armon Rasooli3†, Maryam Amirshahkarami2†, Mohammad Ebrahim Mahdavi2†, Hossein Karshenas2  \n1Faculty of Engineering, Azad University  \n2Faculty of Computer Engineering, University of Isfahan  \n3Department of Electrical Engineering, Iran University of Science and Technology  \n[y.jaliltaheri@iau.ir](y.jaliltaheri@iau.ir), [m.heydari@mehr.ui.ac.ir](m.heydari@mehr.ui.ac.ir), [a.rasouli@ec.iut.ac.ir](a.rasouli@ec.iut.ac.ir)[ ](a.rasouli@ec.iut.ac.ir)[maryamamirshahkarami@mehr.ui.ac.ir](maryamamirshahkarami@mehr.ui.ac.ir), [mhm.ebrh.mahdavi@gmail.com](mhm.ebrh.mahdavi@gmail.com), [h.karshenas@eng.ui.ac.ir](h.karshenas@eng.ui.ac.ir)  \narXiv : 2609 . 1 1206v 1 [cs .AI] 10 Sep 2026  \nAbstract  \nCryptocurrency forecasting presents a distinctive combination of extreme cross-asset scale heterogeneity, nonstationary dynamics, and structural dependencies among Open–High–Low–Close (OHLC) variables. We present CryptoL, a unified framework designed to address these challenges within multivariate time-series forecasting. CryptoL evaluates forecasting error in context-normalized coordinates within the RevIN pipeline, preventing inverse normalization from introducing an additional squared-scale weighting into the MSE objective. We formally characterize this effect through the empirical risk and parameter-gradient geometry, establishing the conditions under which large-scale assets can disproportionately influence shared-model optimization. Beyond lossspace normalization, CryptoL examines channel-independent and channel-dependent normalization for OHLC data, showing that a shared channel-dependent affine transformation preserves candle-order relations that independent channel transformations need not preserve. The framework further incorporates scale-adaptive numerical stabilization to reduce distortions caused by a fixed normalization constant across assets spanning many orders of magnitude, together with a soft feasibility loss that penalizes violations ofthe defining OHLC inequalities. Experiments across heterogeneous cryptocurrency assets evaluate these components through controlled ablationsand demonstrate improvements in forecasting accuracy, training stability, and the frequency of financially valid OHLC predictions relative to the considered baselines. CryptoL therefore provides an integrated approach to scale-balanced optimization, structure-preserving normalization, numerical stabilization, and constraint-aware cryptocurrency forecasting.  \nIntroduction  \nMultivariate financial forecasting using  \nopen–high–low–close (OHLC) data provides a detailed representation of price evolution, but predicting these highly coupled variables jointly is challenging due to abrupt regime changes and strict physical candlestick rules (Das, Goyal,  \n∗These authors contributed equally.  \n†These authors contributed equally.  \nand Yadav 2026; Serdar et al. 2021; Simtharakao 2022; Wang, Huang, and Wang 2021) . This task is especially demanding in cryptocurrency markets, which exhibit extreme non-stationarity and cross-asset scale heterogeneity (Simtharakao 2022; Kim et al. 2021; Berthelier et al. 2026) . Models must learn simultaneously from assets ranging from fractions of a cent to tens of thousands of dollars, making joint optimization difficult when using standard forecasting backbones that struggle with temporal distribution shifts and scale differences (Kim et al. 2021; Liu et al. 2023; Ye et al. 2024; Berthelier et al. 2026; Feng, Huang, and Krompass 2024) .  \nWhile Reversible Instance Normalization (RevIN) is commonly used to mitigate distribution shifts, its implementation details have significant structural and numerical consequences for OHLC data (Kim et al. 2021; Simtharakao 2022; Tepelyan 2025) . Channel-independent standardization can disrupt the relative ordering of candlestick channel","cbCaiq8e2vCsWxfQ","https://ap.wps.com/l/cbCaiq8e2vCsWxfQ","pdf",554164,24,"English","# Abstract\n# Introduction\n## Multivariate financial forecasting with OHLC data\n## Role of RevIN and Two-Phase RevIN (TP-RevIN)\n## Physics constraints and feasibility loss\n## Contributions of the work","[{\"question\":\"What core problem does CryptoL target in cryptocurrency OHLC forecasting?\",\"answer\":\"It targets scale dominance and the preservation of physical candlestick structure while handling nonstationary dynamics and cross-asset heterogeneity across OHLC variables.\"},{\"question\":\"How does CryptoL modify RevIN to reduce unintended scale weighting in MSE?\",\"answer\":\"CryptoL evaluates forecasting error in context-normalized coordinates in the RevIN pipeline, preventing inverse normalization from introducing additional squared-scale weighting into the MSE objective.\"},{\"question\":\"Why does CryptoL include a soft feasibility loss for OHLC predictions?\",\"answer\":\"Because models can still produce financially inadmissible outputs that violate candlestick inequality rules; the auxiliary physics-informed loss penalizes these violations to maintain feasibility.\"}]","CryptoL - Towards Scale Dominance and Physics Constraints Mitigation in Financial Multivariate Time Series Forecasting | PDF",1791838692,8]