Routing Channel-Patch Dependencies in Time Series Forecasting with Graph Spectral Decomposition

2026-03-13

AI Summary

Existing time series forecasting methods struggle to adaptively balance between channel-independent (CI) and channel-dependent (CD) strategies, often leading to insufficient generalization or excessive smoothing of information. To address this limitation, this work proposes xCPD, a novel plug-in module that uniquely integrates spectral decomposition with channel-patch adaptive routing. Specifically, multivariate signals are projected into the frequency domain via the graph Fourier transform, and spectral components are partitioned according to their energy. A frequency-aware expert selection mechanism is then introduced to dynamically modulate the intensity of inter-channel interactions for each patch. This approach enables fine-grained modeling of trends, fluctuations, and abrupt changes, significantly enhancing both prediction accuracy and generalization capability of mainstream models across multiple benchmarks.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Planning, Routing, and Scheduling: Planning/Scheduling and Learning
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Time series forecasting has attracted significant attention in the field of AI. Previous works have revealed that the Channel-Independent (CI) strategy improves forecasting performance by modeling each channel individually, but it often suffers from poor generalization and overlooks meaningful inter-channel interactions. Conversely, Channel-Dependent (CD) strategies aggregate all channels, which may introduce irrelevant information and lead to oversmoothing. Despite recent progress, few existing methods offer the flexibility to adaptively balance CI and CD strategies in response to varying channel dependencies. To address this, we propose a generic plugin xCPD, that can adaptively model the channel-patch dependencies from the perspective of graph spectral decomposition. Specifically, xCPD first projects multivariate signals into the frequency domain using a shared graph Fourier basis, and groups patches into low-, mid-, and high-frequency bands based on their spectral energy responses. xCPD then applies a channel-adaptive routing mechanism that dynamically adjusts the degree of inter-channel interaction for each patch, enabling selective activation of frequency-specific experts. This facilitates fine-grained input-aware modeling of smooth trends, local fluctuations, and abrupt transitions. xCPD can be seamlessly integrated on top of existing CI and CD forecasting models, consistently enhancing both accuracy and generalization across benchmarks. The code is available https://github.com/Clearloveyuan/xCPD.

Problem

• time series forecasting
• channel dependency
• graph spectral decomposition
• adaptive routing
• multivariate time series

Innovation

• graph spectral decomposition
• channel-patch dependency
• frequency-aware routing
• time series forecasting
• adaptive expert activation