  A State Space Model (SSM) is a foundation model in time series analysis,
which has recently been shown as an alternative to transformers in sequence
modeling. In this paper, we theoretically study the generalization of SSMs and
propose improvements to training algorithms based on the generalization
results. Specifically, we give a \textit{data-dependent} generalization bound
for SSMs, showing an interplay between the SSM parameters and the temporal
dependencies of the training sequences. Leveraging the generalization bound, we
(1) set up a scaling rule for model initialization based on the proposed
generalization measure, which significantly improves the robustness of the
output value scales on SSMs to different temporal patterns in the sequence
data; (2) introduce a new regularization method for training SSMs to enhance
the generalization performance. Numerical results are conducted to validate our
results.
