Hiroki Sakamoto

Hiroki Sakamoto, Kazuhiro Sato

This paper develops a data-driven time-limited h2 model reduction method for discrete-time linear time-invariant systems. Specifically, we formulate and solve a regularized time-limited h2 model reduction problem using only noisy impulse response data. Furthermore, we show that the objective function and its gradient can be represented using only noisy impulse response data. Numerical experiments using SLICOT benchmarks demonstrate that the proposed regularized method achieves lower relative time-limited h2 errors than the tested alternatives and is effective in situations where the unregularized method may deteriorate under noise.

Hiroki Sakamoto, Kazuhiro Sato

Deep learning models incorporating linear SSMs have gained attention for capturing long-range dependencies in sequential data. However, their large parameter sizes pose challenges for deployment on resource-constrained devices. In this study, we propose an efficient parameter reduction method for these models by applying $H^{2}$ model order reduction techniques from control theory to their linear SSM components. In experiments, the LRA benchmark results show that the model compression based on our proposed method outperforms an existing method using the Balanced Truncation, while successfully reducing the number of parameters in the SSMs to $1/32$ without sacrificing the performance of the original models.

Hiroki Sakamoto, Kazuhiro Sato

We study deep state-space models (Deep SSMs) that contain linear-quadratic-output (LQO) systems as internal blocks and present a compression method with a provable output error guarantee. We first derive an upper bound on the output error between two Deep SSMs and show that the bound can be expressed via the $h^2$-error norms between the layerwise LQO systems, thereby providing a theoretical justification for existing model order reduction (MOR)-based compression. Building on this bound, we formulate an optimization problem in terms of the $h^2$-error norm and develop a gradient-based MOR method. On the IMDb task from the Long Range Arena benchmark, we demonstrate that our compression method achieves strong performance. Moreover, unlike prior approaches, we reduce roughly 80% of trainable parameters without retraining, with only a 4-5% performance drop.