CPiRi: Channel Permutation-Invariant Relational Interaction for Multivariate Time Series Forecasting

• URL: http://arxiv.org/abs/2601.20318v1
• Date: Wed, 28 Jan 2026 07:30:32 GMT
• Title: CPiRi: Channel Permutation-Invariant Relational Interaction for Multivariate Time Series Forecasting
• Authors: Jiyuan Xu, Wenyu Zhang, Xin Jing, Shuai Chen, Shuai Zhang, Jiahao Nie,
• Abstract summary: Channel-dependent models learn cross-channel features but often overfit the channel ordering.<n>Channel-independent models treat each channel in isolation to increase flexibility, yet this neglects inter-channel dependencies and limits performance.<n>We propose textbfCPiRi, a framework that infers cross-channel structure from data rather than memorizing a fixed ordering.
• Score: 21.579831447953243
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Current methods for multivariate time series forecasting can be classified into channel-dependent and channel-independent models. Channel-dependent models learn cross-channel features but often overfit the channel ordering, which hampers adaptation when channels are added or reordered. Channel-independent models treat each channel in isolation to increase flexibility, yet this neglects inter-channel dependencies and limits performance. To address these limitations, we propose \textbf{CPiRi}, a \textbf{channel permutation invariant (CPI)} framework that infers cross-channel structure from data rather than memorizing a fixed ordering, enabling deployment in settings with structural and distributional co-drift without retraining. CPiRi couples \textbf{spatio-temporal decoupling architecture} with \textbf{permutation-invariant regularization training strategy}: a frozen pretrained temporal encoder extracts high-quality temporal features, a lightweight spatial module learns content-driven inter-channel relations, while a channel shuffling strategy enforces CPI during training. We further \textbf{ground CPiRi in theory} by analyzing permutation equivariance in multivariate time series forecasting. Experiments on multiple benchmarks show state-of-the-art results. CPiRi remains stable when channel orders are shuffled and exhibits strong \textbf{inductive generalization} to unseen channels even when trained on \textbf{only half} of the channels, while maintaining \textbf{practical efficiency} on large-scale datasets. The source code is released at https://github.com/JasonStraka/CPiRi.

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