Title: Mamba Unchained: A Permutation-Invariant Approach to Multivariate Time Series
Primary area: learning on time series and dynamical systems
Keywords: Permutation Invariant, 2D State Space Model, Time Series Modeling

Abstract: Time series data in domains such as climate science, finance, and biomedicine present a significant challenge for scalable modeling due to their multi-scale temporal patterns, complex inter-variable dependencies, and frequency-specific structures. While recent advances in architectures like Transformers and state space models (SSMs) have shown promise, they are often limited by either high computational costs or an inability to capture time-varying cross-variable interactions. To overcome these limitations, we propose a variable-invariant two-dimensional state space model that eliminates variable ordering dependence by leveraging a global, permutation-invariant descriptor to condition temporal dynamics. This design allows for the efficient processing of variable-axis updates through an effective pooling operation, which maintains global correlations and enables full parallelism. We further enhance this architecture with a multi-branch design that incorporates distinct pathways for long- and short-horizon temporal features and a dedicated frequency-domain pathway, all integrated via a lightweight gating mechanism. Through extensive experiments, our model consistently outperforms state-of-the-art baselines on forecasting, classification, and anomaly detection tasks. Comprehensive analysis confirms our model’s efficiency, robustness, and ability to capture diverse temporal–spectral patterns.