Time-Varying Deep State Space Models for Sequences with Switching Dynamics

TL;DR

This paper introduces a neural network-based time-varying state-space model that effectively captures switching dynamics in sequences, outperforming traditional models in synthetic and real-world tasks.

Contribution

It proposes a novel neural network architecture with learnable time-varying dynamics using basis functions, advancing modeling of systems with switching behaviors.

Findings

Outperforms time-invariant models on synthetic switching data

Achieves superior results in speech denoising with switching noise

Provides insights into modeling time-varying dynamics effectively

Abstract

The identification and modeling of time-varying systems is a fundamental challenge in signal processing and system identification. To address this challenge, we propose a class of time-varying state-space model (SSM) based neural networks in which the neurons' states are governed by time-varying dynamics. The proposed model provides the learnable time-varying dynamics through a dictionary of basis functions, where each basis function evolves differently over time. We evaluate the proposed approach on both synthetic data from switching systems and a speech denoising task where real audio is corrupted with switching dynamics noise. The results show that the proposed time-varying model consistently outperforms its time-invariant counterparts while maintaining comparable computational complexity. Our investigations also reveal which aspects of the time-varying dynamics of the data most need to be captured by the proposed time-invariant models, how the additional freedom provided by time-varying basis functions should be allocated across model components, and to what extent larger models can compensate for time-invariant limitations.