Mixture of Projection Experts for Multivariate Long-Term Time Series Forecasting

Multivariate long-term time series forecasting (MLTSF), applicable across various domains, has gained increasing research attention. Channel-independent (CI) models, including Linear and Transformer-based architectures, have recently achieved state-of-the-art (SOTA) performance for MLTSF. Notably, Linear models can deliver satisfactory forecasting performance even with just a single linear projection layer. However, we identify a limitation in this architecture: a single linear projection struggles to adequately capture the inter- and intra-variate heterogeneity in temporal patterns. Similarly, any complex models like Transformer-based models that use a single projection layer to generate final predictions, may face capacity bottlenecks. To overcome this, we propose the Mixture of Projection Experts (MoPE), which replaces the single linear projection with multiple projection branches, and employs a gate network to dynamically assign weights to each branch based on the input data. We applied MoPE to multiple SOTA models and evaluated it on nine real-world datasets. Results show that MoPE boosts forecasting accuracy by an average of 9.59%, demonstrating its effectiveness in mitigating the limitations of a single projection layer. Additionally, our experiments demonstrate that integrating our proposal into CI models enhances their generalization to unseen variates. Interpretability analysis also reveals MoPE's ability to disentangle different temporal patterns. Overall, our paper establishes MoPE as an effective solution for MLTSF tasks.