# Temporally Disentangled Representation Learning under Unknown Nonstationarity

arXiv: https://arxiv.org/abs/2310.18615 · HTML: https://mlsanity.com/paper/2310.18615/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 48 references that are in the map.
- First posted on arXiv 28 Oct 2023.

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

- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [MoCoGAN: Decomposing Motion and Content for Video Generation](https://mlsanity.com/paper/1707.04993/) (2017)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Decomposing Motion and Content for Natural Video Sequence Prediction](https://mlsanity.com/paper/1706.08033/) (2017)
- [Unsupervised Learning of Disentangled Representations from Video](https://mlsanity.com/paper/1705.10915/) (2017)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding](https://mlsanity.com/paper/2007.10930/) (2020)
- [Disentangled Sequential Autoencoder](https://mlsanity.com/paper/1803.02991/) (2018)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Unsupervised Learning of Disentangled and Interpretable Representations from Sequential Data](https://mlsanity.com/paper/1709.07902/) (2017)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series](https://mlsanity.com/paper/2006.12107/) (2020)
- [Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA](https://mlsanity.com/paper/2106.09620/) (2021)
- [S3VAE: Self-Supervised Sequential VAE for Representation Disentanglement and Data Generation](https://mlsanity.com/paper/2005.11437/) (2020)
- [Temporally Disentangled Representation Learning](https://mlsanity.com/paper/2210.13647/) (2022)
- [AdaRL: What, Where, and How to Adapt in Transfer Reinforcement Learning](https://mlsanity.com/paper/2107.02729/) (2021)
- [Inference via low-dimensional couplings](https://mlsanity.com/paper/1703.06131/) (2017)
- [Contrastively Disentangled Sequential Variational Autoencoder](https://mlsanity.com/paper/2110.12091/) (2021)
- [Multifactor Sequential Disentanglement via Structured Koopman Autoencoders](https://mlsanity.com/paper/2303.17264/) (2023)
- [Disentangled Recurrent Wasserstein Autoencoder](https://mlsanity.com/paper/2101.07496/) (2021)
- [Turning Normalizing Flows into Monge Maps with Geodesic Gaussian Preserving Flows](https://mlsanity.com/paper/2209.10873/) (2022)

## Built on by (most cited first, 22 of 22)

- [Marrying Causal Representation Learning with Dynamical Systems for Science](https://mlsanity.com/paper/2405.13888/) (2024)
- [Causal Temporal Representation Learning with Nonstationary Sparse Transition](https://mlsanity.com/paper/2409.03142/) (2024)
- [LLM Interpretability with Identifiable Temporal-Instantaneous Representation](https://mlsanity.com/paper/2509.23323/) (2025)
- [From Orthogonality to Dependency: Learning Disentangled Representation for Multi-Modal Time-Series Sensing Signals](https://mlsanity.com/paper/2405.16083/) (2024)
- [Modeling Unseen Environments with Language-guided Composable Causal Components in Reinforcement Learning](https://mlsanity.com/paper/2505.08361/) (2025)
- [TRACE: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning](https://mlsanity.com/paper/2601.21135/) (2026)
- [Disentangling Long-Short Term State Under Unknown Interventions for Online Time Series Forecasting](https://mlsanity.com/paper/2502.12603/) (2025)
- [Revealing Multimodal Causality with Large Language Models](https://mlsanity.com/paper/2509.17784/) (2025)
- [Disentangling Dynamical Systems: Causal Representation Learning Meets Local Sparse Attention](https://mlsanity.com/paper/2603.14483/) (2026)
- [Online Time Series Forecasting with Theoretical Guarantees](https://mlsanity.com/paper/2510.18281/) (2025)
- [Causal Representation Meets Stochastic Modeling under Generic Geometry](https://mlsanity.com/paper/2602.05033/) (2026)
- [Causal View of Time Series Imputation: Some Identification Results on Missing Mechanism](https://mlsanity.com/paper/2505.07180/) (2025)
- [Understanding Catastrophic Interference: On the Identifibility of Latent Representations](https://mlsanity.com/paper/2509.23027/) (2025)
- [MOSAIC: Module Discovery via Sparse Additive Identifiable Causal Learning for Scientific Time Series](https://mlsanity.com/paper/2605.05524/) (2026)
- [End-to-End Identifiable and Consistent Recurrent Switching Dynamical Systems](https://mlsanity.com/paper/2605.06315/) (2026)
- [Identifying latent state transition in non-linear dynamical systems](https://mlsanity.com/paper/2406.03337/) (2024)
- [Incorporating Interventional Independence Improves Robustness against Interventional Distribution Shift](https://mlsanity.com/paper/2507.05412/) (2025)
- [DRL-STAF: A Deep Reinforcement Learning Framework for State-Aware Forecasting of Complex Multivariate Hidden Markov Processes](https://mlsanity.com/paper/2605.14632/) (2026)
- [Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts](https://mlsanity.com/paper/2606.28228/) (2026)
- [I Act Therefore I Am: When Is JEPA's Action-Conditioning Enough to Learn Causal Mechanisms?](https://mlsanity.com/paper/2609.31161/) (2026)
- [Towards Identifiable Representations under Misspecified Structure](https://mlsanity.com/paper/2609.33273/) (2026)
- [Causal Representation Learning with Instantaneous and Lagged Relations via Nonstationarity](https://mlsanity.com/paper/2610.03452/) (2026)

## Abstract (arXiv)

In unsupervised causal representation learning for sequential data with time-delayed latent causal influences, strong identifiability results for the disentanglement of causally-related latent variables have been established in stationary settings by leveraging temporal structure. However, in nonstationary setting, existing work only partially addressed the problem by either utilizing observed auxiliary variables (e.g., class labels and/or domain indexes) as side information or assuming simplified latent causal dynamics. Both constrain the method to a limited range of scenarios. In this study, we further explored the Markov Assumption under time-delayed causally related process in nonstationary setting and showed that under mild conditions, the independent latent components can be recovered from their nonlinear mixture up to a permutation and a component-wise transformation, without the observation of auxiliary variables. We then introduce NCTRL, a principled estimation framework, to reconstruct time-delayed latent causal variables and identify their relations from measured sequential data only. Empirical evaluations demonstrated the reliable identification of time-delayed latent causal influences, with our methodology substantially outperforming existing baselines that fail to exploit the nonstationarity adequately and then, consequently, cannot distinguish distribution shifts.