# Causal Temporal Representation Learning with Nonstationary Sparse Transition

arXiv: https://arxiv.org/abs/2409.03142 · HTML: https://mlsanity.com/paper/2409.03142/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 73 references that are in the map.
- First posted on arXiv 5 Sep 2024.

## Builds on (most cited first, 30 of 45)

- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [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)
- [Cross-task weakly supervised learning from instructional videos](https://mlsanity.com/paper/1903.08225/) (2019)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [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)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [Hierarchical Deep Temporal Models for Group Activity Recognition](https://mlsanity.com/paper/1607.02643/) (2016)
- [On the Identifiability of Nonlinear ICA: Sparsity and Beyond](https://mlsanity.com/paper/2206.07751/) (2022)
- [Actor-Transformers for Group Activity Recognition](https://mlsanity.com/paper/2003.12737/) (2020)
- [D3TW: Discriminative Differentiable Dynamic Time Warping for Weakly Supervised Action Alignment and Segmentation](https://mlsanity.com/paper/1901.02598/) (2019)
- [Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series](https://mlsanity.com/paper/2006.12107/) (2020)
- [Weakly-Supervised Action Segmentation with Iterative Soft Boundary Assignment](https://mlsanity.com/paper/1803.10699/) (2018)
- [Connectionist Temporal Modeling for Weakly Supervised Action Labeling](https://mlsanity.com/paper/1607.08584/) (2016)
- [Weakly Supervised Action Learning with RNN based Fine-to-coarse Modeling](https://mlsanity.com/paper/1703.08132/) (2017)
- [Causal Representation Learning from Multiple Distributions: A General Setting](https://mlsanity.com/paper/2402.05052/) (2024)
- [NeuralNetwork-Viterbi: A Framework for Weakly Supervised Video Learning](https://mlsanity.com/paper/1805.06875/) (2018)
- [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)
- [Weakly Supervised Energy-Based Learning for Action Segmentation](https://mlsanity.com/paper/1909.13155/) (2019)
- [Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems](https://mlsanity.com/paper/2206.06169/) (2022)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [Weakly Supervised Action Labeling in Videos Under Ordering Constraints](https://mlsanity.com/paper/1407.1208/) (2014)
- [AdaRL: What, Where, and How to Adapt in Transfer Reinforcement Learning](https://mlsanity.com/paper/2107.02729/) (2021)
- [Weakly supervised learning of actions from transcripts](https://mlsanity.com/paper/1610.02237/) (2016)
- [Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependencies](https://mlsanity.com/paper/2401.04890/) (2024)

## Built on by (most cited first, 13 of 13)

- [Thought Communication in Multiagent Collaboration](https://mlsanity.com/paper/2510.20733/) (2025)
- [LLM Interpretability with Identifiable Temporal-Instantaneous Representation](https://mlsanity.com/paper/2509.23323/) (2025)
- [TRACE: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning](https://mlsanity.com/paper/2601.21135/) (2026)
- [Unsupervised Representation Learning from Sparse Transformation Analysis](https://mlsanity.com/paper/2410.05564/) (2024)
- [Causal Representation Meets Stochastic Modeling under Generic Geometry](https://mlsanity.com/paper/2602.05033/) (2026)
- [Hierarchical Action Learning for Weakly-Supervised Action Segmentation](https://mlsanity.com/paper/2602.24275/) (2026)
- [Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing](https://mlsanity.com/paper/2604.13218/) (2026)
- [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)
- [Infant Cry Detection Using Causal Temporal Representation](https://mlsanity.com/paper/2503.06247/) (2025)
- [Linear Causal Representation Learning by Topological Ordering, Pruning, and Disentanglement](https://mlsanity.com/paper/2509.22553/) (2025)
- [Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts](https://mlsanity.com/paper/2606.28228/) (2026)
- [Causal Representation Learning with Instantaneous and Lagged Relations via Nonstationarity](https://mlsanity.com/paper/2610.03452/) (2026)

## Abstract (arXiv)

Causal Temporal Representation Learning (Ctrl) methods aim to identify the temporal causal dynamics of complex nonstationary temporal sequences. Despite the success of existing Ctrl methods, they require either directly observing the domain variables or assuming a Markov prior on them. Such requirements limit the application of these methods in real-world scenarios when we do not have such prior knowledge of the domain variables. To address this problem, this work adopts a sparse transition assumption, aligned with intuitive human understanding, and presents identifiability results from a theoretical perspective. In particular, we explore under what conditions on the significance of the variability of the transitions we can build a model to identify the distribution shifts. Based on the theoretical result, we introduce a novel framework, Causal Temporal Representation Learning with Nonstationary Sparse Transition (CtrlNS), designed to leverage the constraints on transition sparsity and conditional independence to reliably identify both distribution shifts and latent factors. Our experimental evaluations on synthetic and real-world datasets demonstrate significant improvements over existing baselines, highlighting the effectiveness of our approach.