[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86017-en":3,"doc-seo-86017-105":30,"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":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},86017,1099514067415,"Rowan","https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502",8,"Research & Report","Multi-Scale Convolution with Optimal Transport Attention Effect on Multivariate Time Series","Multi-Scale Convolution with Optimal Transport (MSC-OT) is introduced to improve multivariate time series (MTS) forecasting by modeling multi-granularity structural patterns while suppressing noise. The architecture integrates multi-scale convolution into attention score matrices built from inverted embedding, which treats each variable as a token to strengthen cross-variate relationships. It further formulates attention as an entropy-regularized optimal transport problem solved via Sinkhorn iterations for balanced information flow. An adaptive fusion mechanism combines base, convolution-enhanced, and OT-regularized scores, achieving strong results on ETT, Electricity, Traffic, Solar-Energy, and Exchange-Rate, supported by ablation studies.","Multi-Scale Convolution with Optimal Transport Attention Effect on Multivariate Time Series  \n1st HaoChong Fu Institute of Collaborative Innovation University of Macau Macau, China [fantaisiedemickey@gmail.com](fantaisiedemickey@gmail.com)  \n2nd Jian Xu RIKEN AIP Tokyo, Japan [jian.xu@riken.jp](jian.xu@riken.jp)  \narXiv :2607 . 10740v 1 [ cs .LG] 12 Jul 2026  \nAbstract—The analysis of Multivariate Time Series (MTS) plays an important role in a lot of real-world practical applications, but it still remains some challenging problem about capturing multi-granularity structural patterns and suppressing noise appropriately. Multi-Scale Convolution with Optimal Transport Attention (MSC-OT) is proposed in this paper. MSCOT is a useful architecture to optimize the attention mechanism. It combines multi-scale convolution with Sinkhorn optimal transport method based on inverted embedding. The inverted embedding approach embeds each variable as a token and allows the model to capture cross-variate relationships better. MSC-OT consists of two part: (1) Multi-Scale Convolution Enhancement, that applies multi-scale convolutions to attention score matrices based on inverted embedding, capturing local structural patterns in the variate-interaction space induced by compressed temporal representations; (2) Sinkhorn Optimal Transport Regularization, that formulates attention computation as an optimal transport problem and employs iterative matrix scaling to ensure balanced information flow across variates. Adaptive Fusion Strategy utilizes softmax-normalized learnable weights to dynamically combine base attention, convolution-enhanced, and OT-regularized scores. Experiments on widely-used datasets, including ETT, Electricity, Traffic, Solar-Energy, and Exchange-Rate, show that MSC-OT achieves well performance in both short-term and longterm forecasting tasks. Ablation experiments further validate the effectiveness of each proposed component and their synergistic contributions to improving prediction accuracy for multivariate time series forecasting.  \nIndex Terms—multivariate time series, multi-scale convolution, optimal transport, attention optimization.  \nI. INTRODUCTION  \nTransformer [1] has achieved a success in natural language processing [2] and computer vision [3], emerging as the dominant architecture for sequence modeling tasks. Inspired by this success, Transformer-based models have been extensively adapted for time series forecasting, with different type of innovations including sparse attention mechanisms [4], auto-correlation decomposition [5], and frequency-enhanced representations [6] .  \nBut researchers have recently questioned the validity of conventional Transformer-based forecasters, which typically embed multiple variates of the same time into channels and apply attention on temporal tokens. Considering the numerical but less semantic relationship among time points, simple linear layers have been shown to exceed complicated Transformers  \non both performance and efficiency [7] . ITransformer [8] addressed it by introducing an inverted embedding paradigm that embeds entire time series of each variate as a single token. This type of embedding enable the attention mechanism to explicitly capture cross-variate dependencies rather than temporal dependencies. However, we observe that the inverted embedding paradigm raises a critical limitation: by embedding each variate’s temporal information into a fixed-dimensional token, fine-grained temporal patterns important to prediction may be lost.  \nFig. 1. In MSC-OT, we use α to define the base score weighting, β to define the Multi-Scale Convolution weighting, γ to define the Sinkhorn Optimal Transport weighting, and the final result is calculated using an adaptive fusion algorithm.  \nConsidering these limitations, we focus on how to enhance the inverted embedding framework while preserving its advantages for cross-variate modeling. MSC-OT (MultiScale Convolution with Optimal Transport)","cbCaifKwbZayLNgh","https://ap.wps.com/l/cbCaifKwbZayLNgh","pdf",647746,3,1,7,"English","en",105,"# Introduction\n## Motivation for inverted embedding enhancement\n## Proposed MSC-OT attention mechanism\n# Related Works","[{\"question\":\"What problem does MSC-OT address in multivariate time series forecasting?\",\"answer\":\"MSC-OT targets difficulties in capturing multi-granularity structural patterns and suppressing noise, especially limitations introduced by inverted embedding for cross-variate modeling.\"},{\"question\":\"How does MSC-OT use inverted embedding in its attention design?\",\"answer\":\"Inverted embedding represents each variable’s entire time series as a single token, enabling the model to capture dependencies across variables rather than focusing only on temporal token relationships.\"},{\"question\":\"How is optimal transport incorporated into MSC-OT attention computation?\",\"answer\":\"MSC-OT formulates attention as an entropy-regularized optimal transport problem and applies the Sinkhorn algorithm to obtain doubly-stochastic attention distributions that improve robustness to anomalous noise.\"}]",1784207818,18,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":28},"multi-scale-convolution-with-optimal-transport-attention-effect-on-multivariate-time-series","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"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":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/multi-scale-convolution-with-optimal-transport-attention-effect-on-multivariate-time-series/86017/",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","2026-07-27","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 problem does MSC-OT address in multivariate time series forecasting?","Question",{"text":75,"@type":76},"MSC-OT targets difficulties in capturing multi-granularity structural patterns and suppressing noise, especially limitations introduced by inverted embedding for cross-variate modeling.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does MSC-OT use inverted embedding in its attention design?",{"text":80,"@type":76},"Inverted embedding represents each variable’s entire time series as a single token, enabling the model to capture dependencies across variables rather than focusing only on temporal token relationships.",{"name":82,"@type":73,"acceptedAnswer":83},"How is optimal transport incorporated into MSC-OT attention computation?",{"text":84,"@type":76},"MSC-OT formulates attention as an entropy-regularized optimal transport problem and applies the Sinkhorn algorithm to obtain doubly-stochastic attention distributions that improve robustness to anomalous 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