Compression Method for Deep Diagonal State Space Model Based on $H^2$ Optimal Reduction

TL;DR

This paper introduces an $H^2$ optimal reduction technique for compressing deep diagonal state space models, significantly reducing parameters while maintaining performance, thus enabling deployment on resource-limited devices.

Contribution

It applies $H^2$ model order reduction from control theory to deep linear SSMs, achieving superior compression compared to existing methods.

Findings

Model parameters reduced to 1/32 without performance loss.

Outperforms Balanced Truncation in benchmark tests.

Enables efficient deployment on resource-constrained devices.

Abstract

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.