Chimera: Effectively Modeling Multivariate Time Series with
  2-Dimensional State Space Models
Authors: name: Ali Behrouz, name: Michele Santacatterina, name: Ramin Zabih

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.