Recent deep models for multivariate time series (MTS) forecasting highlight Transformer-based approaches for capturing long-term (cross-temporal) dependencies. However, most of these models impose uniform transformations across heterogeneous dimensions, failing to capture cross-dimensional dependencies that are crucial for MTS forecasting. Furthermore, the quadratic complexity \(O(L^2)\) of the attention mechanism creates an unbearable computational bottleneck when processing long historical sequences. To address these challenges, we propose Crossmamba, a novel Mamba-empowered architecture featuring three key innovations: (1) The MamMLP module exploits Mamba’s selective state space paradigm to achieve linear time complexity for MTS processing; (2) The Full Dimensional State Extraction (FDSE) layer combines linear time series modeling with dimension-aware dependency learning; (3) The Spectral Noising (SN) technique injects frequency-band-specific perturbations to simulate real-world non-stationarity and periodicity. The main structure of the architecture is the Spectral Noising Encoder–Decoder (SNED). It starts with Time Cycle Embedding, which vectorizes the original MTS data into a 2D vector array with time and dimension information. Subsequently, the encoder of the SNED, which is built by multiple FDSE layers and SN layers, processes these to generate multi-granular representations enhanced by simulating non-stationary and periodic changes. The decoder of the SNED transforms these multi-granular representations and accumulates them to obtain the final prediction result. Extensive experimental results demonstrate the effectiveness of Crossmamba over previous techniques. Code is available at https://github.com/IHAN-1212/Crossmamba.
