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Recent foundation models improve transfer across tasks, but many rely on centralized data and Transformer attention, limiting use for long, high-dimensional, and privacy-sensitive signals. This paper introduces QuantFlow, a probabilistic framework combining inverted sequence embedding, bidirectional Mamba state-space decoders, quantile regression, and federated learning with non-IID clients. Results show strong accuracy on ETTm1 and Weather and preserve performance after multiple communication rounds without centralizing raw records.",{"@graph":69,"@context":122},[70,84,105],{"@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/quantflow-a-federated-mamba-based-post-transformer-foundation-model-for-time-series-forecasting/327549/",{"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/quantflow-a-federated-mamba-based-post-transformer-foundation-model-for-time-series-forecasting/327549.png","ImageObject",300,407,{"name":92,"@type":93},"Maeve","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-26","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does QuantFlow address in time-series forecasting?","Question",{"text":112,"@type":113},"QuantFlow targets limitations of time-series foundation models that often require centralized data and Transformer attention, which hinder use for long, high-dimensional, and privacy-sensitive signals.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does QuantFlow produce probabilistic forecasts?",{"text":117,"@type":113},"It uses quantile regression to project predictions to conditional quantiles, enabling median forecasts and prediction intervals.",{"name":119,"@type":110,"acceptedAnswer":120},"How is federated learning applied in QuantFlow?",{"text":121,"@type":113},"The method evaluates a multi-client, non-IID federated setup where clients train locally and communicate model updates without transmitting raw observations, maintaining useful accuracy after several rounds.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},327549,1791154539,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":34,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144,"preview_page_count":4},5909877438554,"https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272","QuantFlow: A Federated Mamba-Based Post-Transformer Foundation Model  \nfor Time-Series Forecasting  \nShah Nawaz Haider 1, Steve Austin 1, Arnab Barua 2, Sarowar Morshed Shawon 2, Hadaate Ullah 3  \n1 Department of Computer Science and Engineering, University of Science and Technology Chittagong  \n2 Department of Electrical and Electronic Engineering, University of Science and Technology Chittagong  \n3 Faculty of Science, Engineering and Technology, University of Science and Technology Chittagong [nawazhaider60@gmail.com](nawazhaider60@gmail.com), [steve_austin_@outlook.com](steve_austin_@outlook.com), [arnab.me@outlook.com](arnab.me@outlook.com), [shawon@ustc.ac.bd](shawon@ustc.ac.bd), [hadaate@ustc.ac.bd](hadaate@ustc.ac.bd)  \nAbstract  \nTime-series forecasting supports decisions in finance, energy, transportation, public health, and industrial monitoring. Recent foundation models improve transfer across forecasting tasks, but many depend on centralized data and Transformer attention, which restricts their use for long, high-dimensional, and privacy-sensitive signals. This paper presents QuantFlow, a probabilistic forecasting framework that combines inverted sequence embedding, bidirectional Mamba state-space decoders, quantile regression, and federated learning. Each variable is embedded over the complete observation window, processed in forward and reverse directions, and projected to five conditional quantiles. TSMixup expands temporal diversity through Dirichlet-weighted interpolation while preserving sequence structure. Experiments cover cryptocurrency, traffic, electricity, Electricity Transformer Temperature, influenza, and weather data. QuantFlow obtains mean squared errors of 0.2834 on ETTm1 and 0.2218 on Weather, and a 20-client non-IID deployment retains useful accuracy after three communication rounds without centralizing raw records. The results indicate that selective statespace modelling is a promising basis for scalable, uncertainty-aware, and privacy-conscious time-series prediction, while also revealing limitations on irregular epidemiological signals and long-horizon generalization.  \nCode: [https://github.com/nawaz0x1/QuantFlow](https://github.com/nawaz0x1/QuantFlow)  \n1 Introduction  \nArtificial intelligence is reinventing forecasting by learning the intricate temporal patterns in data, artificial-intelligencedriven time-series forecasting tools have the potential to be applied in virtually every industry. However, more recent deep learning (DL) technologies have enabled improved forecasting of time series data that is so extensive, and yet often so volatile, as to have been intractable using classical statistical approaches. Addressing these, foundation model (FM) work by having reusable representations that are learned across heterogeneous large datasets instead of rebuilding task-specific models from scratch. This principle benefits time-series forecasting since organizations repeatedly predict various figures such as stock prices, electrical demand, traffic occupancy, disease prevalence, equipment  \nstatus, or weather data. This approach could also reduce manual feature engineering and offer a consistent forecasting interface. Even so, the existing time series FM faces three challenges which hinders its practical use:  \nComputational scalability: Since most time-series FM are based on Transformer attention, and both memory and computation cost increase with data dimension and context size.  \nData locality: Since the diverse datasets used to train most foundations models can be distributed among organizations, who may not be able to share raw observations due to regulations, security, ownership or privacy.  \nFederated learning (FL) resolves the data locality issue through local training and global model aggregation rather than sharing raw data, while it does not address the computational bottleneck since it relies on the same communication of updates as in centralized settings (McMahan et al. 2017). Sel","cbCaiptKNAslwme7","https://ap.wps.com/l/cbCaiptKNAslwme7","pdf",464387,"English","# Abstract\n# 1 Introduction\n# 2 Related Work\n## 2.1 Deep and Probabilistic Forecasting","[{\"question\":\"What problem does QuantFlow address in time-series forecasting?\",\"answer\":\"QuantFlow targets limitations of time-series foundation models that often require centralized data and Transformer attention, which hinder use for long, high-dimensional, and privacy-sensitive signals.\"},{\"question\":\"How does QuantFlow produce probabilistic forecasts?\",\"answer\":\"It uses quantile regression to project predictions to conditional quantiles, enabling median forecasts and prediction intervals.\"},{\"question\":\"How is federated learning applied in QuantFlow?\",\"answer\":\"The method evaluates a multi-client, non-IID federated setup where clients train locally and communicate model updates without transmitting raw observations, maintaining useful accuracy after several rounds.\"}]","QuantFlow - A Federated Mamba-Based Post-Transformer Foundation Model for Time-Series Forecasting | PDF",1789977497,18]