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

2026-01-28

AI Summary

This work addresses the tension in multivariate time series forecasting between modeling inter-channel dependencies and preserving model flexibility: channel-dependent approaches are prone to overfitting due to sensitivity to channel ordering, while channel-independent models neglect inter-channel relationships. To resolve this, we propose CPiRi, a novel framework that introduces permutation invariance over channels into multivariate time series modeling for the first time. CPiRi employs a spatiotemporal decoupling architecture, a frozen pre-trained temporal encoder, a lightweight spatial relation module, and a channel-shuffling training strategy to adaptively infer channel relationships from data. Grounded in permutation equivariance theory, our approach ensures strong inductive generalization to unseen channel configurations. Experiments demonstrate that CPiRi achieves state-of-the-art performance across multiple benchmarks, exhibits robustness to channel order perturbations, generalizes to full-channel settings using only half the channels during training, and maintains efficiency at scale.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Computer Vision: Multi-modal Vision
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

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.

Problem

• multivariate time series forecasting
• channel permutation invariance
• cross-channel dependencies
• inductive generalization
• structural co-drift

Innovation

• Channel Permutation Invariance
• Spatio-temporal Decoupling
• Inductive Generalization
• Permutation Equivariance
• Multivariate Time Series Forecasting