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A variety of real-world applications rely on far future information to makedecisions, thus calling for efficient and accurate long sequence multivariatetime series forecasting. While recent attention-based forecasting models showstrong abilities in capturing long-term dependencies, they still suffer fromtwo key limitations. First, canonical self attention has a quadratic complexityw.r.t. the input time series length, thus falling short in efficiency. Second,different variables' time series often have distinct temporal dynamics, whichexisting studies fail to capture, as they use the same model parameter space,e.g., projection matrices, for all variables' time series, thus falling shortin accuracy. To ensure high efficiency and accuracy, we propose Triformer, atriangular, variable-specific attention. (i) Linear complexity: we introduce anovel patch attention with linear complexity. When stacking multiple layers ofthe patch attentions, a triangular structure is proposed such that the layersizes shrink exponentially, thus maintaining linear complexity. (ii)Variable-specific parameters: we propose a light-weight method to enabledistinct sets of model parameters for different variables' time series toenhance accuracy without compromising efficiency and memory usage. Strongempirical evidence on four datasets from multiple domains justifies our designchoices, and it demonstrates that Triformer outperforms state-of-the-artmethods w.r.t. both accuracy and efficiency. This is an extended version of"Triformer: Triangular, Variable-Specific Attentions for Long SequenceMultivariate Time Series Forecasting", to appear in IJCAI 2022 [Cirstea et al.,2022a], including additional experimental results.

Triformer: Triangular, Variable-Specific Attentions for Long Sequence Multivariate Time Series Forecasting--Full Version