Sequential Order-Robust Mamba for Time Series Forecasting

Mamba has recently emerged as a promising alternative to Transformers, offering near-linear complexity in processing sequential data. However, while channels in time series (TS) data have no specific order in general, recent studies have adopted Mamba to capture channel dependencies (CD) in TS, introducing a sequential order bias. To address this issue, we propose SOR-Mamba, a TS forecasting method that 1) incorporates a regularization strategy to minimize the discrepancy between two embedding vectors generated from data with reversed channel orders, thereby enhancing robustness to channel order, and 2) eliminates the 1D-convolution originally designed to capture local information in sequential data. Furthermore, we introduce channel correlation modeling (CCM), a pretraining task aimed at preserving correlations between channels from the data space to the latent space in order to enhance the ability to capture CD. Extensive experiments demonstrate the efficacy of the proposed method across standard and transfer learning scenarios. Time series (TS) forecasting is prevalent in various fields, including weather (Angryk et al., 2020), traffic (Cirstea et al., 2022), and energy (Dudek et al., 2021). While Transformers (Vaswani et al., 2017) have been widely employed for this task due to their ability to capture long-term dependencies in sequences (Wen et al., 2022), their quadratic computational complexity causes substantial computational overhead, limiting their practicality in real-world applications.