From Generalization Analysis to Optimization Designs for State Space Models
This work addresses the challenge of optimizing SSMs for better generalization in sequence modeling, offering incremental improvements to training algorithms based on theoretical insights.
The authors tackled the problem of improving generalization in State Space Models (SSMs) by deriving a data-dependent generalization bound and using it to design a scaling rule for initialization and a new regularization method, resulting in enhanced robustness and performance validated through numerical experiments.
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.