KARMA: A Multilevel Decomposition Hybrid Mamba Framework for Multivariate Long-Term Time Series Forecasting

2025-06-10

AI Summary

To address the rigidity of conventional decomposition methods and the low modeling efficiency of Transformers in multivariate long-term time series forecasting, this paper proposes a hierarchical adaptive decomposition and Mamba-based collaborative modeling framework. We innovatively design Adaptive Temporal-Channel Decomposition (ATCD) and Hybrid Frequency-Time Decomposition (HFTD) to jointly and adaptively disentangle trend, seasonal, and frequency-domain features. Furthermore, we introduce the multi-scale KarmaBlock—a unified module integrating learnable temporal decomposition, frequency-domain transformation, state-space modeling (Mamba), multi-scale convolution, and gating mechanisms—to enhance global-local dynamic representation. Evaluated on eight real-world, cross-domain benchmark datasets, our method achieves an average 9.2% improvement in forecasting accuracy and 3.8× faster inference speed compared to state-of-the-art Transformer-based approaches.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

Multivariate long-term and efficient time series forecasting is a key requirement for a variety of practical applications, and there are complex interleaving time dynamics in time series data that require decomposition modeling. Traditional time series decomposition methods are single and rely on fixed rules, which are insufficient for mining the potential information of the series and adapting to the dynamic characteristics of complex series. On the other hand, the Transformer-based models for time series forecasting struggle to effectively model long sequences and intricate dynamic relationships due to their high computational complexity. To overcome these limitations, we introduce KARMA, with an Adaptive Time Channel Decomposition module (ATCD) to dynamically extract trend and seasonal components. It further integrates a Hybrid Frequency-Time Decomposition module (HFTD) to further decompose Series into frequency-domain and time-domain. These components are coupled with multi-scale Mamba-based KarmaBlock to efficiently process global and local information in a coordinated manner. Experiments on eight real-world datasets from diverse domains well demonstrated that KARMA significantly outperforms mainstream baseline methods in both predictive accuracy and computational efficiency. Code and full results are available at this repository: https://github.com/yedadasd/KARMA

Problem

• Dynamic decomposition of multivariate long-term time series
• Overcoming Transformer limitations in modeling long sequences
• Enhancing predictive accuracy and computational efficiency

Innovation

• Adaptive Time Channel Decomposition module
• Hybrid Frequency-Time Decomposition module
• Multi-scale Mamba-based KarmaBlock