[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82395-en":3,"doc-seo-82395-105":29,"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":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82395,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","GatedLinear: Adaptive Routing of Complementary Linear Bases for Time Series Forecasting","Time series forecasting must model diverse, sometimes mutually exclusive temporal dynamics, from smooth trend continuation to nonstationary drift and phase-aligned recurrence. Many deep models force these patterns through a single backbone with fixed inductive biases, limiting performance under real-world heterogeneity across variables and horizons. GatedLinear introduces adaptive routing among three complementary linear bases: global trend-seasonal projection, difference-based incremental drift, and phase-indexed cyclic reuse. A Tri-Factorized Fusion Gate produces horizon- and phase-aware, channel-specific routing decisions, enabling fine-grained soft selection without heavy neural stacking. Experiments on standard benchmarks show state-of-the-art or highly competitive accuracy with fewer parameters.","arXiv :2607 .09537v 1 [ cs .LG] 10 Jul 2026  \nGatedLinear: Adaptive Routing of Complementary Linear Bases for Time Series Forecasting  \nQitai Tan, Ruiwen Gu, Yilin Su, Mo Li, Xu Lin, Xiao-Ping Zhang†  \nShenzhen Key Laboratory of Ubiquitous Data Enabling, Shenzhen International Graduate School, Tsinghua University [tqt24@mails.tsinghua.edu.cn](tqt24@mails.tsinghua.edu.cn)  \n[xpzhang@ieee.org](xpzhang@ieee.org)  \nAbstract  \nTime series forecasting requires models to capture diverse, often mutually exclusive, temporal dynamics, from smooth trend continuation to nonstationary drift and strict phase-aligned recurrence. While recent deep learning models have improved accuracy, they typically force these diverse patterns through a single computational backbone governed by fixed algorithmic inductive biases (e.g., self-attention or spectral filtering) . This single-mechanism approach often struggles with the profound heterogeneity of real-world series, where different variables and forecast horizons necessitate fundamentally different predictive treatments. To address this, we propose GatedLinear: a lightweight framework that frames forecasting asthe adaptive routing of complementary linear bases. GatedLinear leverages a pool of three specialized mechanisms: a global trend-seasonal basis for smooth projection, a difference-based incremental basis for nonstationary drift, and a phasealigned recurrence basis for explicit cyclic reuse. To dynamically orchestrate these distinct behaviors, we introduce a Tri-Factorized Fusion Gate that disentangles routing decisions into channel-specific preferences, horizon-aware offsets, and phase-indexed biases derived from known future time marks. This design allows the model to perform highly granular, point-wise soft routing across different predictive regimes without stacking computationally heavy neural modules. Experiments on standard benchmarks show that our method achieves state-of-the-art or highly competitive accuracy against recent complex foundational models, while offering explicitly interpretable routing patterns and operating with a substantially smaller parameter footprint.  \n1 Introduction  \nTime series forecasting is a fundamental problem in many real-world systems, including energy management, traffic control, weather prediction, finance, and industrial monitoring. The central challenge is not merely to fit historical observations, but to extrapolate future values under multiple temporal mechanisms. A future trajectory may continue a smooth trend, evolve through short-term increments, repeat a phase-aligned periodic pattern (i.e., exact historical recurring points such as 2:00 PM daily), or combine these behaviors in different proportions across variables and forecast horizons.  \nPreviously, time series forecasting predominantly relied on classical statistical models, such as ARIMA [1], vector autoregression (VAR) [2], and exponential smoothing (ETS) [3] . With the rise of deep learning, early neural approaches further advanced the field, including RNN-based DeepAR [4], LSTNet [5], and SegRNN [6], as well as CNN-based TCN [7] and SCINet [8] . More  \nrecently, the continuing advancement of deep learning has derived several prominent branches that †Corresponding author.  \nPreprint.  \nFigure 1: Trait heterogeneity in time series forecasting benchmarks. (a) Different datasets exhibit distinct profiles across temporal traits, suggesting that no single forecasting mechanism is uniformly appropriate across datasets. (b) Even within one dataset, variable channels can have broad trait distributions, indicating substantial channel-level heterogeneity. The six temporal traits are defined in the Appendix D.  \nsteer the development of the field. Linear and MLP-based methods (e.g., DLinear [9], TimeMixer [10], TimeAlign [11]) pursue lightweight forecasting by emphasizing trend–seasonal decomposition, multi-scale mixing, or distribution-aware alignment. Transformer-based techniques (e.g., Autoformer","cbCaivgQWXONV7py","https://ap.wps.com/l/cbCaivgQWXONV7py","pdf",7440601,1,29,"English","en",105,"# Introduction\n## Problem of temporal heterogeneity\n## Limitations of single-mechanism backbones\n## Overview of related forecasting approaches","[{\"question\":\"What motivates GatedLinear for time series forecasting?\",\"answer\":\"Real-world time series contain heterogeneous and sometimes mutually exclusive temporal dynamics (trend continuation, nonstationary drift, and phase-aligned recurrence). A single fixed forecasting mechanism often cannot handle all pattern types well, motivating adaptive routing across specialized bases.\"},{\"question\":\"How does GatedLinear model different temporal dynamics?\",\"answer\":\"It uses a pool of three specialized linear bases: a global trend-seasonal basis for smooth projection, a difference-based incremental basis for nonstationary drift, and a phase-aligned recurrence basis for explicit cyclic reuse.\"},{\"question\":\"How are routing decisions computed in GatedLinear?\",\"answer\":\"A Tri-Factorized Fusion Gate disentangles routing into channel-specific preferences, horizon-aware offsets, and phase-indexed biases derived from known future time marks, enabling point-wise soft routing across predictive regimes.\"}]",1784180106,73,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"gatedlinear-adaptive-routing-of-complementary-linear-bases-for-time-series-forecasting","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/gatedlinear-adaptive-routing-of-complementary-linear-bases-for-time-series-forecasting/82395/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","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 motivates GatedLinear for time series forecasting?","Question",{"text":75,"@type":76},"Real-world time series contain heterogeneous and sometimes mutually exclusive temporal dynamics (trend continuation, nonstationary drift, and phase-aligned recurrence). A single fixed forecasting mechanism often cannot handle all pattern types well, motivating adaptive routing across specialized bases.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does GatedLinear model different temporal dynamics?",{"text":80,"@type":76},"It uses a pool of three specialized linear bases: a global trend-seasonal basis for smooth projection, a difference-based incremental basis for nonstationary drift, and a phase-aligned recurrence basis for explicit cyclic reuse.",{"name":82,"@type":73,"acceptedAnswer":83},"How are routing decisions computed in GatedLinear?",{"text":84,"@type":76},"A Tri-Factorized Fusion Gate disentangles routing into channel-specific preferences, horizon-aware offsets, and phase-indexed biases derived from known future time marks, enabling point-wise soft routing across predictive regimes.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]