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.

翻译：当前多元时间序列预测方法可分为通道依赖型与通道独立型模型。通道依赖模型虽能学习跨通道特征，但常过度拟合通道顺序，导致在通道增减或重排时难以适应。通道独立模型将各通道独立处理以提升灵活性，却忽略了通道间依赖关系，限制了预测性能。为克服这些局限，本文提出 \textbf{CPiRi}——一种\textbf{通道置换不变（CPI）}框架，其从数据中推断跨通道结构而非记忆固定顺序，从而能在结构与分布协同漂移的场景中直接部署而无需重新训练。CPiRi 将\textbf{时空解耦架构}与\textbf{置换不变正则化训练策略}相结合：冻结的预训练时序编码器提取高质量时序特征，轻量级空间模块学习内容驱动的通道间关系，而通道混洗策略在训练中强制实现 CPI。我们进一步通过分析多元时间序列预测中的置换等变性，\textbf{为 CPiRi 奠定理论基础}。在多个基准数据集上的实验取得了最先进的结果。CPiRi 在通道顺序重排时保持稳定，即使在\textbf{仅使用半数通道}训练的情况下，对未见通道仍展现出强大的\textbf{归纳泛化}能力，同时在大规模数据集上保持\textbf{实用高效性}。源代码已发布于 https://github.com/JasonStraka/CPiRi。