C-Mamba: Channel Correlation Enhanced State Space Models for Multivariate Time Series Forecasting

In recent years, significant progress has been made in multivariate time series forecasting using Linear-based, Transformer-based, and Convolution-based models. However, these approaches face notable limitations: linear forecasters struggle with representation capacities, attention mechanisms suffer from quadratic complexity, and convolutional models have a restricted receptive field. These constraints impede their effectiveness in modeling complex time series, particularly those with numerous variables. Additionally, many models adopt the Channel-Independent (CI) strategy, treating multivariate time series as uncorrelated univariate series while ignoring their correlations. For models considering inter-channel relationships, whether through the self-attention mechanism, linear combination, or convolution, they all incur high computational costs and focus solely on weighted summation relationships, neglecting potential proportional relationships between channels. In this work, we address these issues by leveraging the newly introduced state space model and propose \textbf{C-Mamba}, a novel approach that captures cross-channel dependencies while maintaining linear complexity without losing the global receptive field. Our model consists of two key components: (i) channel mixup, where two channels are mixed to enhance the training sets; (ii) channel attention enhanced patch-wise Mamba encoder that leverages the ability of the state space models to capture cross-time dependencies and models correlations between channels by mining their weight relationships. Our model achieves state-of-the-art performance on seven real-world time series datasets. Moreover, the proposed mixup and attention strategy exhibits strong generalizability across other frameworks.