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

Authors: Dongyuan Li, Shun Zheng, Chang Xu, Jiang Bian, Renhe Jiang Date: 2026-03-14 Paper ID: openalex:2603.13702

Summary

This paper introduces xCPD, a plug-and-play module designed to dynamically resolve the trade-off between Channel-Independent (CI) and Channel-Dependent (CD) modeling in time series forecasting. xCPD employs graph spectral decomposition to transform the input into the frequency domain, where signal patches are categorized into low, mid, and high-frequency bands based on spectral energy. A subsequent channel-adaptive routing mechanism then selectively engages experts tailored to these frequency bands, allowing for input-aware control over inter-channel interactions. This approach enables the model to capture smooth trends (low-frequency), local fluctuations (mid-frequency), and abrupt changes (high-frequency) effectively. The module consistently enhances the performance of underlying forecasting models across diverse benchmarks.

Key Contributions

• Proposes xCPD, a generic plugin that adaptively models channel-patch dependencies using graph spectral decomposition to balance CI and CD modeling strategies.
• 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 spectral energy.
• Introduces a channel-adaptive routing mechanism that dynamically adjusts inter-channel interaction for each patch by activating frequency-specific experts, enabling fine-grained modeling of trends, fluctuations, and transitions.
• Demonstrates that xCPD can be seamlessly integrated with existing CI/CD forecasting models, consistently improving accuracy and generalization across various benchmarks.

Limitations

The description focuses heavily on the mechanism and mentions consistent enhancement across benchmarks, but specific quantitative results or comparisons against state-of-the-art baselines (statistical or deep learning) are not detailed in the abstract.

Open Questions & Future Work

• incorporating-external-domain-knowledge-in-spectral-grouping
• adaptive-interpretable-graph-filtering-strategies
• expanding-plugin-applicability-structured-prediction
• integrating-spectral-modeling-foundation-models

Key Concepts

• Channel-Patch Dependencies Routing: A mechanism that adaptively balances Channel-Independent (CI) and Channel-Dependent (CD) modeling by leveraging graph spectral decomposition to route information based on patch frequency bands.

Limitations

The description focuses heavily on the mechanism and mentions consistent enhancement across benchmarks, but specific quantitative results or comparisons against state-of-the-art baselines (statistical or deep learning) are not detailed in the abstract.

Links

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