{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/vcformer-variable-correlation-transformer","title":"VCformer: Variable Correlation Transformer with Inherent Lagged Correlation for Multivariate Time Series Forecasting","arxiv_id":"2405.11470","date":"2024-05-19","proceeding":null,"authors":["Yingnan Yang","Qingling Zhu","Jianyong Chen"],"abstract":"Multivariate time series (MTS) forecasting has been extensively applied across diverse domains, such as weather prediction and energy consumption. However, current studies still rely on the vanilla point-wise self-attention mechanism to capture cross-variable dependencies, which is inadequate in extracting the intricate cross-correlation implied between variables. To fill this gap, we propose Variable Correlation Transformer (VCformer), which utilizes Variable Correlation Attention (VCA) module to mine the correlations among variables. Specifically, based on the stochastic process theory, VCA calculates and integrates the cross-correlation scores corresponding to different lags between queries and keys, thereby enhancing its ability to uncover multivariate relationships. Additionally, inspired by Koopman dynamics theory, we also develop Koopman Temporal Detector (KTD) to better address the non-stationarity in time series. The two key components enable VCformer to extract both multivariate correlations and temporal dependencies. Our extensive experiments on eight real-world datasets demonstrate the effectiveness of VCformer, achieving top-tier performance compared to other state-of-the-art baseline models. Code is available at this repository: https://github.com/CSyyn/VCformer.","url_abs":"https://arxiv.org/abs/2405.11470v1","url_pdf":"https://arxiv.org/pdf/2405.11470v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"vcformer-variable-correlation-transformer","repo_url":"https://github.com/csyyn/vcformer","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"multivariate-time-series-forecasting","task_name":"Multivariate Time Series Forecasting"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series-forecasting","task_name":"Time Series Forecasting"}],"methods":[{"method_slug":"absolute-position-encodings","method_name":"Absolute Position Encodings"},{"method_slug":"adam","method_name":"Adam"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"bpe","method_name":"BPE"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"label-smoothing","method_name":"Label Smoothing"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"position-wise-feed-forward-layer","method_name":"Position-Wise Feed-Forward Layer"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"transformer","method_name":"Transformer"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/time-series-forecasting-on-etth1-336-1","task":"Time Series Forecasting","dataset":"ETTh1 (336) Multivariate","model":"VCformer","rank_in_archive_order":53,"of":72,"metrics":{"MAE":"0.449","MSE":"0.473"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2405.11470","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2405.11470"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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