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Enhancing Channel-Independent Time Series Forecasting via Cross-Variate Patch Embedding

Donghwa Shin, Edwin Zhang

TL;DR

This work introduces Cross-Variate Patch Embedding (CVPE) to augment channel-independent time series forecasting, enabling cross-variate information to be learned without redesigning the entire model. By enriching patch embeddings with a learnable position encoding and a router-attention block, CVPE injects inter-variable context into Time-LLM while preserving its CI backbone. Empirical results on seven real-world datasets show CVPE can improve forecasting on datasets with strong inter-variate correlations (e.g., Weather, Modified Traffic) but may cause overfitting and degradation on datasets with weaker correlations (e.g., ETTh2, ETTm2). The findings highlight a promising direction for balancing cross-variable modeling with robustness in CI architectures and point to future work on larger backbones and alternative cross-variate mechanisms.

Abstract

Transformers have recently gained popularity in time series forecasting due to their ability to capture long-term dependencies. However, many existing models focus only on capturing temporal dependencies while omitting intricate relationships between variables. Recent models have tried tackling this by explicitly modeling both cross-time and cross-variate dependencies through a sequential or unified attention mechanism, but they are entirely channel dependent (CD) across all layers, making them potentially susceptible to overfitting. To address this, we propose Cross-Variate Patch Embeddings (CVPE), a lightweight CD module that injects cross-variate context into channel-independent (CI) models by simply modifying the patch embedding process. We achieve this by adding a learnable positional encoding and a lightweight router-attention block to the vanilla patch embedding layer. We then integrate CVPE into Time-LLM, a multimodal CI forecasting model, to demonstrate its effectiveness in capturing cross-variate dependencies and enhance the CI model's performance. Extensive experimental results on seven real-world datasets show that our enhanced Time-LLM outperforms the original baseline model simply by incorporating the CVPE module, with no other changes.

Enhancing Channel-Independent Time Series Forecasting via Cross-Variate Patch Embedding

TL;DR

This work introduces Cross-Variate Patch Embedding (CVPE) to augment channel-independent time series forecasting, enabling cross-variate information to be learned without redesigning the entire model. By enriching patch embeddings with a learnable position encoding and a router-attention block, CVPE injects inter-variable context into Time-LLM while preserving its CI backbone. Empirical results on seven real-world datasets show CVPE can improve forecasting on datasets with strong inter-variate correlations (e.g., Weather, Modified Traffic) but may cause overfitting and degradation on datasets with weaker correlations (e.g., ETTh2, ETTm2). The findings highlight a promising direction for balancing cross-variable modeling with robustness in CI architectures and point to future work on larger backbones and alternative cross-variate mechanisms.

Abstract

Transformers have recently gained popularity in time series forecasting due to their ability to capture long-term dependencies. However, many existing models focus only on capturing temporal dependencies while omitting intricate relationships between variables. Recent models have tried tackling this by explicitly modeling both cross-time and cross-variate dependencies through a sequential or unified attention mechanism, but they are entirely channel dependent (CD) across all layers, making them potentially susceptible to overfitting. To address this, we propose Cross-Variate Patch Embeddings (CVPE), a lightweight CD module that injects cross-variate context into channel-independent (CI) models by simply modifying the patch embedding process. We achieve this by adding a learnable positional encoding and a lightweight router-attention block to the vanilla patch embedding layer. We then integrate CVPE into Time-LLM, a multimodal CI forecasting model, to demonstrate its effectiveness in capturing cross-variate dependencies and enhance the CI model's performance. Extensive experimental results on seven real-world datasets show that our enhanced Time-LLM outperforms the original baseline model simply by incorporating the CVPE module, with no other changes.
Paper Structure (21 sections, 3 equations, 2 figures, 4 tables)

This paper contains 21 sections, 3 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Brief Overview of Time-LLM
  5. Cross-Variate Patch Embedding Overview
  6. Rationale
  7. Experiments
  8. Long-Term Forecasting Results
  9. Datasets
  10. Setup
  11. Results
  12. Conclusion and Future Work
  13. Detailed Overview of Time-LLM Architecture
  14. Input Embedding
  15. Patch Reprogramming
  16. ...and 6 more sections

Figures (2)

  • Figure 1: Model framework of Time-LLM with CVPE. Red dotted line represents original Time-LLM pipeline with the vanilla patch embedding; Green represents modified Time-LLM with CVPE module. As shown in the figure, no other modification is made to Time-LLM.
  • Figure 2: Visualization of router-attention mechanism, inspired by zhang2023crossformer. Given position-aware patch embedding $\overline{\mathbf{X}}_P$, a small set of $c$ routers aggregate information from all variates, then redistribute it back to create enhanced embeddings with cross-variate information.