{"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/the-capacity-and-robustness-trade-off","title":"The Capacity and Robustness Trade-off: Revisiting the Channel Independent Strategy for Multivariate Time Series Forecasting","arxiv_id":"2304.05206","date":"2023-04-11","proceeding":null,"authors":["Lu Han","Han-Jia Ye","De-Chuan Zhan"],"abstract":"Multivariate time series data comprises various channels of variables. The multivariate forecasting models need to capture the relationship between the channels to accurately predict future values. However, recently, there has been an emergence of methods that employ the Channel Independent (CI) strategy. These methods view multivariate time series data as separate univariate time series and disregard the correlation between channels. Surprisingly, our empirical results have shown that models trained with the CI strategy outperform those trained with the Channel Dependent (CD) strategy, usually by a significant margin. Nevertheless, the reasons behind this phenomenon have not yet been thoroughly explored in the literature. This paper provides comprehensive empirical and theoretical analyses of the characteristics of multivariate time series datasets and the CI/CD strategy. Our results conclude that the CD approach has higher capacity but often lacks robustness to accurately predict distributionally drifted time series. In contrast, the CI approach trades capacity for robust prediction. Practical measures inspired by these analyses are proposed to address the capacity and robustness dilemma, including a modified CD method called Predict Residuals with Regularization (PRReg) that can surpass the CI strategy. We hope our findings can raise awareness among researchers about the characteristics of multivariate time series and inspire the construction of better forecasting models.","url_abs":"https://arxiv.org/abs/2304.05206v1","url_pdf":"https://arxiv.org/pdf/2304.05206v1.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":"the-capacity-and-robustness-trade-off","repo_url":"https://github.com/hanlu-nju/channel_independent_mtsf","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"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":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2304.05206","atlas_url":"https://app.syntology.ai/?focus=2304.05206","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2304.05206"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/hanlu-nju/channel_independent_mtsf","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran_fixture":1,"unverified":2},"by_repo_kind":{"official":{"samples":3,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":3,"samples":[{"code_sha256_prefix":"a54c8c5c47c6a8b8","entry":"phi_","repo":"hanlu-nju/channel_independent_mtsf","repo_kind":"official","path":"layers/utils.py","file_url":"https://github.com/hanlu-nju/channel_independent_mtsf/blob/HEAD/layers/utils.py","link_basis":"harvester_set","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":false,"mcp_get_code":{"code_sha256":"a54c8c5c47c6a8b8"}},{"code_sha256_prefix":"13917795f8030166","entry":"test","repo":"hanlu-nju/channel_independent_mtsf","repo_kind":"official","path":"layers/utils.py","file_url":"https://github.com/hanlu-nju/channel_independent_mtsf/blob/HEAD/layers/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":false,"mcp_get_code":{"code_sha256":"13917795f8030166"}},{"code_sha256_prefix":"6a37a43acaf3b4b1","entry":"train","repo":"hanlu-nju/channel_independent_mtsf","repo_kind":"official","path":"layers/utils.py","file_url":"https://github.com/hanlu-nju/channel_independent_mtsf/blob/HEAD/layers/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":false,"mcp_get_code":{"code_sha256":"6a37a43acaf3b4b1"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}