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

arXiv: https://arxiv.org/abs/2605.06315 · HTML: https://mlsanity.com/paper/2605.06315/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 49 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 26 of 26)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding](https://mlsanity.com/paper/2007.10930/) (2020)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [Normalizing Flows are Capable Generative Models](https://mlsanity.com/paper/2412.06329/) (2024)
- [Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series](https://mlsanity.com/paper/2006.12107/) (2020)
- [Identifiability of deep generative models without auxiliary information](https://mlsanity.com/paper/2206.10044/) (2022)
- [Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA](https://mlsanity.com/paper/2106.09620/) (2021)
- [Temporally Disentangled Representation Learning](https://mlsanity.com/paper/2210.13647/) (2022)
- [Reconstructing regime-dependent causal relationships from observational time series](https://mlsanity.com/paper/2007.00267/) (2020)
- [Collapsed Amortized Variational Inference for Switching Nonlinear Dynamical Systems](https://mlsanity.com/paper/1910.09588/) (2019)
- [Temporally Disentangled Representation Learning under Unknown Nonstationarity](https://mlsanity.com/paper/2310.18615/) (2023)
- [Independent Innovation Analysis for Nonlinear Vector Autoregressive Process](https://mlsanity.com/paper/2006.10944/) (2020)
- [Switching Linear Dynamics for Variational Bayes Filtering](https://mlsanity.com/paper/1905.12434/) (2019)
- [Deep Explicit Duration Switching Models for Time Series](https://mlsanity.com/paper/2110.13878/) (2021)
- [Causal Temporal Representation Learning with Nonstationary Sparse Transition](https://mlsanity.com/paper/2409.03142/) (2024)
- [Causal Discovery from Conditionally Stationary Time Series](https://mlsanity.com/paper/2110.06257/) (2021)
- [Graph Switching Dynamical Systems](https://mlsanity.com/paper/2306.00370/) (2023)
- [On the Identifiability of Switching Dynamical Systems](https://mlsanity.com/paper/2305.15925/) (2023)

## Built on by (most cited first, 1 of 1)

- [Explainable Wastewater Digital Twins: Adaptive Context-Conditioned Structured Simulators with Self-Falsifying Decision Support](https://mlsanity.com/paper/2605.19826/) (2026)

## Abstract (arXiv)

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 OmegaSDS, 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 OmegaSDS achieves improved disentanglement compared to VAE-based estimators and more accurate forecasting of underlying dynamics.