Chimera: Effectively Modeling Multivariate Time Series with 2-Dimensional State Space Models

TL;DR

Chimera introduces a novel 2D state space model framework for multivariate time series that captures complex dependencies and seasonal patterns more effectively than traditional models, with improved efficiency and broad applicability.

Contribution

The paper proposes Chimera, a 2D SSM-based approach with input-dependent heads and a fast training method, advancing modeling of complex multivariate time series.

Findings

Outperforms existing models on diverse benchmarks

Effectively captures seasonal and long-term dependencies

Demonstrates superior accuracy in classification, forecasting, and anomaly detection

Abstract

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due to their simplicity and expressive power to represent linear dependencies. They, however, have fundamentally limited expressive power to capture non-linear dependencies, are slow in practice, and fail to model the inter-variate information flow. Despite recent attempts to improve the expressive power of SSMs by using deep structured SSMs, the existing methods are either limited to univariate time series, fail to model complex patterns (e.g., seasonal patterns), fail to dynamically model the dependencies of variate and time dimensions, and/or are input-independent. We present Chimera that uses two input-dependent 2-D SSM heads with different discretization processes to learn long-term progression and seasonal patterns. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. We further present and discuss 2-dimensional Mamba and Mamba-2 as the spacial cases of our 2D SSM. Our experimental evaluation shows the superior performance of Chimera on extensive and diverse benchmarks, including ECG and speech time series classification, long-term and short-term time series forecasting, and time series anomaly detection.