# CaRiNG: Learning Temporal Causal Representation under Non-Invertible Generation Process

arXiv: https://arxiv.org/abs/2401.14535 · HTML: https://mlsanity.com/paper/2401.14535/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 61 references that are in the map.
- First posted on arXiv 25 Jan 2024.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Quo Vadis, Action Recognition? A New Model and the Kinetics Dataset](https://mlsanity.com/paper/1705.07750/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [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)
- [Hierarchical Conditional Relation Networks for Video Question Answering](https://mlsanity.com/paper/2002.10698/) (2020)
- [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)
- [Sequential Neural Models with Stochastic Layers](https://mlsanity.com/paper/1605.07571/) (2016)
- [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)
- [SUTD-TrafficQA: A Question Answering Benchmark and an Efficient Network for Video Reasoning over Traffic Events](https://mlsanity.com/paper/2103.15538/) (2021)
- [Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series](https://mlsanity.com/paper/2006.12107/) (2020)
- [Latent Normalizing Flows for Discrete Sequences](https://mlsanity.com/paper/1901.10548/) (2019)
- [Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA](https://mlsanity.com/paper/2106.09620/) (2021)
- [Cross-Modal Causal Relational Reasoning for Event-Level Visual Question Answering](https://mlsanity.com/paper/2207.12647/) (2022)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [DualVGR: A Dual-Visual Graph Reasoning Unit for Video Question Answering](https://mlsanity.com/paper/2107.04768/) (2021)
- [Attend What You Need: Motion-Appearance Synergistic Networks for Video Question Answering](https://mlsanity.com/paper/2106.10446/) (2021)
- [Multifactor Sequential Disentanglement via Structured Koopman Autoencoders](https://mlsanity.com/paper/2303.17264/) (2023)
- [COMPOSER: Compositional Reasoning of Group Activity in Videos with Keypoint-Only Modality](https://mlsanity.com/paper/2112.05892/) (2021)

## Built on by (most cited first, 23 of 23)

- [NeuroClips: Towards High-fidelity and Smooth fMRI-to-Video Reconstruction](https://mlsanity.com/paper/2410.19452/) (2024)
- [On the Identification of Temporally Causal Representation with Instantaneous Dependence](https://mlsanity.com/paper/2405.15325/) (2024)
- [Causal Temporal Representation Learning with Nonstationary Sparse Transition](https://mlsanity.com/paper/2409.03142/) (2024)
- [Towards Identifiability of Hierarchical Temporal Causal Representation Learning](https://mlsanity.com/paper/2510.18310/) (2025)
- [Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis](https://mlsanity.com/paper/2501.12500/) (2025)
- [LLM Interpretability with Identifiable Temporal-Instantaneous Representation](https://mlsanity.com/paper/2509.23323/) (2025)
- [Learning Causal Domain-Invariant Temporal Dynamics for Few-Shot Action Recognition](https://mlsanity.com/paper/2402.12706/) (2024)
- [Synergy Between Sufficient Changes and Sparse Mixing Procedure for Disentangled Representation Learning](https://mlsanity.com/paper/2503.00639/) (2025)
- [CausalVerse: Benchmarking Causal Representation Learning with Configurable High-Fidelity Simulations](https://mlsanity.com/paper/2510.14049/) (2025)
- [TRACE: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning](https://mlsanity.com/paper/2601.21135/) (2026)
- [Controllable Video Generation with Provable Disentanglement](https://mlsanity.com/paper/2502.02690/) (2025)
- [Discovering Latent Causal Graphs from Spatiotemporal Data](https://mlsanity.com/paper/2411.05331/) (2024)
- [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)
- [SemVideo: Reconstructs What You Watch from Brain Activity via Hierarchical Semantic Guidance](https://mlsanity.com/paper/2602.21819/) (2026)
- [Hierarchical Action Learning for Weakly-Supervised Action Segmentation](https://mlsanity.com/paper/2602.24275/) (2026)
- [Should Bias be Eliminated? A General Framework to Use Bias for OOD Generalization](https://mlsanity.com/paper/2507.17001/) (2025)
- [Diverse Dictionary Learning](https://mlsanity.com/paper/2604.17568/) (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)
- [Causal Representation Learning with Instantaneous and Lagged Relations via Nonstationarity](https://mlsanity.com/paper/2610.03452/) (2026)
- [Identifiable World Models from Pretrained Diffusion Representations](https://mlsanity.com/paper/2610.07028/) (2026)
- [Prospective Forcing: Learning to Look Ahead for Autoregressive Long Video Diffusion](https://mlsanity.com/paper/2610.14654/) (2026)

## Abstract (arXiv)

Identifying the underlying time-delayed latent causal processes in sequential data is vital for grasping temporal dynamics and making downstream reasoning. While some recent methods can robustly identify these latent causal variables, they rely on strict assumptions about the invertible generation process from latent variables to observed data. However, these assumptions are often hard to satisfy in real-world applications containing information loss. For instance, the visual perception process translates a 3D space into 2D images, or the phenomenon of persistence of vision incorporates historical data into current perceptions. To address this challenge, we establish an identifiability theory that allows for the recovery of independent latent components even when they come from a nonlinear and non-invertible mix. Using this theory as a foundation, we propose a principled approach, CaRiNG, to learn the CAusal RepresentatIon of Non-invertible Generative temporal data with identifiability guarantees. Specifically, we utilize temporal context to recover lost latent information and apply the conditions in our theory to guide the training process. Through experiments conducted on synthetic datasets, we validate that our CaRiNG method reliably identifies the causal process, even when the generation process is non-invertible. Moreover, we demonstrate that our approach considerably improves temporal understanding and reasoning in practical applications.