title: Chimera: Effectively Modeling Multivariate Time Series with
    2-Dimensional State Space Models
summary: 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.
paper_authors._id: 66627923a5e2fb9d6b6ecc7a
paper_authors.name: Ali Behrouz
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2024-06-07T09:19:50.227Z
paper_authors._id: 65cccd5134a5d74cbaa9446c
paper_authors.avatarUrl: /avatars/5255b734628992106598eae4f2c5848f.svg
paper_authors.fullname: Ali Behrouz
paper_authors.type: user
paper_authors.user: AliBehrouz
paper_authors._id: 66627923a5e2fb9d6b6ecc7b
paper_authors.name: Michele Santacatterina
paper_authors._id: 66627923a5e2fb9d6b6ecc7c
paper_authors.name: Ramin Zabih
paper_title: Chimera: Effectively Modeling Multivariate Time Series with
    2-Dimensional State Space Models
paper_summary: 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.
paper_ai_keywords: State Space Models (SSMs) deep structured SSMs univariate time series input-dependent 2-D SSM heads discretization processes 2-dimensional parallel selective scan long-term progression seasonal patterns 2-dimensional Mamba and M-2 spacial cases of our 2D SSM ECG and speech time series classification long-term and short-term time series forecasting time series anomaly detection