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CATS-Linear: Classification Auxiliary Linear Model for Time Series Forecasting

Zipo Jibao, Yingyi Fu, Xinyang Chen, Guoting Chen

TL;DR

The paper tackles multivariate time series forecasting when different series mappings can be heterogeneous. It introduces Classification Auxiliary Channel-Independence (CACI) to route samples to category-specific predictors and refines DLinear by decoupling seasonal and trend information into TSLinear with complex-domain seasonality and trend decoupling, all trained under an error-supervised scheme with RevIN normalization. Theoretical analysis compares channel designs and derives excess-risk bounds, highlighting CACI’s bias-variance trade-offs and its $O(1)$ parameter scaling with respect to the feature dimension. Empirically, CATS-Linear achieves state-of-the-art performance with fixed hyperparameters across seven benchmarks, offering improved accuracy and efficiency over tuned baselines and standard channel designs. The work demonstrates that tuning-free, architecture-agnostic routing combined with advanced linear decompositions yields robust, scalable forecasting with practical impact for real-world sequence modeling.

Abstract

Recent research demonstrates that linear models achieve forecasting performance competitive with complex architectures, yet methodologies for enhancing linear models remain underexplored. Motivated by the hypothesis that distinct time series instances may follow heterogeneous linear mappings, we propose the Classification Auxiliary Trend-Seasonal Decoupling Linear Model CATS-Linear, employing Classification Auxiliary Channel-Independence (CACI). CACI dynamically routes instances to dedicated predictors via classification, enabling supervised channel design. We further analyze the theoretical expected risks of different channel settings. Additionally, we redesign the trend-seasonal decomposition architecture by adding a decoupling -- linear mapping -- recoupling framework for trend components and complex-domain linear projections for seasonal components. Extensive experiments validate that CATS-Linear with fixed hyperparameters achieves state-of-the-art accuracy comparable to hyperparameter-tuned baselines while delivering SOTA accuracy against fixed-hyperparameter counterparts.

CATS-Linear: Classification Auxiliary Linear Model for Time Series Forecasting

TL;DR

The paper tackles multivariate time series forecasting when different series mappings can be heterogeneous. It introduces Classification Auxiliary Channel-Independence (CACI) to route samples to category-specific predictors and refines DLinear by decoupling seasonal and trend information into TSLinear with complex-domain seasonality and trend decoupling, all trained under an error-supervised scheme with RevIN normalization. Theoretical analysis compares channel designs and derives excess-risk bounds, highlighting CACI’s bias-variance trade-offs and its parameter scaling with respect to the feature dimension. Empirically, CATS-Linear achieves state-of-the-art performance with fixed hyperparameters across seven benchmarks, offering improved accuracy and efficiency over tuned baselines and standard channel designs. The work demonstrates that tuning-free, architecture-agnostic routing combined with advanced linear decompositions yields robust, scalable forecasting with practical impact for real-world sequence modeling.

Abstract

Recent research demonstrates that linear models achieve forecasting performance competitive with complex architectures, yet methodologies for enhancing linear models remain underexplored. Motivated by the hypothesis that distinct time series instances may follow heterogeneous linear mappings, we propose the Classification Auxiliary Trend-Seasonal Decoupling Linear Model CATS-Linear, employing Classification Auxiliary Channel-Independence (CACI). CACI dynamically routes instances to dedicated predictors via classification, enabling supervised channel design. We further analyze the theoretical expected risks of different channel settings. Additionally, we redesign the trend-seasonal decomposition architecture by adding a decoupling -- linear mapping -- recoupling framework for trend components and complex-domain linear projections for seasonal components. Extensive experiments validate that CATS-Linear with fixed hyperparameters achieves state-of-the-art accuracy comparable to hyperparameter-tuned baselines while delivering SOTA accuracy against fixed-hyperparameter counterparts.

Paper Structure

This paper contains 11 sections, 4 theorems, 8 equations, 3 figures, 6 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORK
  3. METHODOLOGY
  4. Classification Auxiliary Paradigm
  5. Feature Decoupling Linear Model
  6. Training Schema
  7. Theoretical Analysis
  8. EXPERIMENTS
  9. Main Results
  10. Ablation Study
  11. Conclusion

Key Result

Lemma 1

We have $\mathcal{R^*} = \sigma^2$ and $\mathcal{R}(\theta) -\mathcal{R^*} = \Vert \theta - \theta^* \Vert^2_{\Psi}$ for any $\theta \in \Theta$, where $\Vert \theta \Vert^2_{\Psi} = \frac{1}{N}\theta^T\Psi\theta$ is a Mahalanobis distance norm. Particularly, if $\hat{\theta}$ is a random variable s

Figures (3)

  • Figure 1: Schematic illustration of the two mainstream channel designs.
  • Figure 2: Pipeline of CATS-Linear with TSLinear as predictors and RevIN as normalization method.
  • Figure 3: Visualization of the 10 complex linear weights' modulus in CATS-Linear, from left to right. The downward-sloping lines indicate that data periodicity induces corresponding periodicity in model weights.

Theorems & Definitions (8)

  • Definition 1: Expected Risk
  • Lemma 1: Risk Decomposition
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3: Trend Decoupling
  • proof