Channel-Dependent State Space Model for Multivariate Time Series Forecasting
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wu-ycw1031-sm-eecs-2026-thesis.pdf
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Author(s)
Wu, Yu-Cheng
Advisor(s)
Boning, Duane S.
Date Issued
May 2026
Publisher
Massachusetts Institute of Technology
Abstract
Accurate multivariate time series forecasting (MTSF) is crucial for decision-making in complex, interconnected temporal systems across diverse domains, including manufacturing, energy, finance, meteorology, transportation, and healthcare. With the rapid advances in deep learning, recent state-of-the-art methods typically rely on a single neural network to model all time series jointly and can be broadly divided into two categories. Channel-independent strategies provide strong baselines by focusing exclusively on temporal dynamics, partly because inter-series correlations are empirically weak on most benchmarks. In contrast, channel-dependent approaches attempt to learn meaningful relationships along both dimensions, but typically rely on heuristic inductive biases, especially structural compromises, to prevent overfitting and improve generalization, since time series data are inherently noisier and less abundant in practice than other modalities such as text and images.
To address these limitations, this thesis proposes Chameleon, a novel channel-dependent state space model (SSM) that enables data-dependent and fine-grained cross-series interaction on a sequential architecture naturally suited to time series. Building on GatedDeltaNet, a recent extension of SSMs, this work recognizes its favorable inductive biases for time series and adapts it into a further specialized backbone through targeted design choices, including reversible instance normalization with stochastic perturbation and a lightweight decomposition-based embedding. Beyond these adaptations, this work establishes a theoretical connection between selective SSMs and the Kalman filter, under which each temporal patch token plays a dual role: as a control input for the intra-series “time update” and as an observation signal for the “measurement update” across variables. By refining hidden states through a learnable Kalman gain at each step, Chameleon adjusts its predictions using local cross-series information. Experiments on standard long-horizon benchmarks show that Chameleon outperforms prior leading models in 23 and 16 of 28 cases for mean squared error (MSE) and mean absolute error (MAE), respectively. Further experiments on two distinct, strongly correlated datasets, PEMS08 and Double Pendulum, validate the effectiveness of the proposed cross-series mechanism. Together, these results establish Chameleon as a scalable, theoretically grounded, and empirically effective framework for MTSF.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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