End-to-End Identifiable and Consistent Recurrent Switching Dynamical Systems

2026-05-07

AI Summary

This work addresses the limitations of existing methods that rely on stationarity assumptions and restrictive emission models, which hinder the learning of identifiable representations from dynamical sequences with state switches. To overcome this, the authors propose an end-to-end identifiable and consistent modeling framework for recurrent switching dynamical systems. Under milder assumptions, they theoretically establish identifiability for nonlinear recurrent switching systems and avoid variational approximations by employing a flow-based ΩSDS estimator combined with an expectation–maximization algorithm to enable exact likelihood optimization. Experiments demonstrate that the proposed method outperforms VAEs on both synthetic and real-world data, achieving superior performance in disentangled representation learning and accurate prediction of underlying dynamics.

Abstract

Learning identifiable representations in deep generative models remains a fundamental challenge, particularly for sequential data with regime-switching dynamics. Existing approaches establish identifiability under restrictive assumptions, such as stationarity or limited emission models, and typically rely on variational autoencoder (VAE) estimators, which introduce approximation gaps that limit the recovery of the latent structure. In this work, we address both the theoretical and practical limitations of this setting. First, we establish identifiability of a broad class of recurrent nonlinear switching dynamical systems under flexible assumptions, significantly extending prior results. Second, we introduce $Ω$SDS, a flow-based estimator that enables exact likelihood optimization using expectation-maximisation. Through empirical validation on both synthetic and real-world data, our results demonstrate that $Ω$SDS achieves improved disentanglement compared to VAE-based estimators and more accurate forecasting of underlying dynamics.

Problem

• identifiability
• switching dynamical systems
• sequential data
• deep generative models
• latent structure recovery

Innovation

• identifiability
• switching dynamical systems
• flow-based estimation
• expectation-maximisation
• disentanglement