# Causal Representation Learning with Instantaneous and Lagged Relations via Nonstationarity

arXiv: https://arxiv.org/abs/2610.03452 · HTML: https://mlsanity.com/paper/2610.03452/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 24 of 24)

- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [On human motion prediction using recurrent neural networks](https://mlsanity.com/paper/1705.02445/) (2017)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [Deep representation learning for human motion prediction and classification](https://mlsanity.com/paper/1702.07486/) (2017)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Causal Representation Learning from Multiple Distributions: A General Setting](https://mlsanity.com/paper/2402.05052/) (2024)
- [Temporally Disentangled Representation Learning](https://mlsanity.com/paper/2210.13647/) (2022)
- [Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems](https://mlsanity.com/paper/2206.06169/) (2022)
- [Causal Representation Learning Made Identifiable by Grouping of Observational Variables](https://mlsanity.com/paper/2310.15709/) (2023)
- [CaRiNG: Learning Temporal Causal Representation under Non-Invertible Generation Process](https://mlsanity.com/paper/2401.14535/) (2024)
- [From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modeling](https://mlsanity.com/paper/2310.11011/) (2023)
- [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)
- [Generative Causal Representation Learning for Out-of-Distribution Motion Forecasting](https://mlsanity.com/paper/2302.08635/) (2023)
- [Causal Temporal Representation Learning with Nonstationary Sparse Transition](https://mlsanity.com/paper/2409.03142/) (2024)
- [Towards Interpretable Deep Generative Models via Causal Representation Learning](https://mlsanity.com/paper/2504.11609/) (2025)
- [Towards Identifiability of Hierarchical Temporal Causal Representation Learning](https://mlsanity.com/paper/2510.18310/) (2025)
- [LLM Interpretability with Identifiable Temporal-Instantaneous Representation](https://mlsanity.com/paper/2509.23323/) (2025)
- [Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families](https://mlsanity.com/paper/2606.02231/) (2026)

## Abstract (arXiv)

Causal representation learning for time-series data aims to identify latent states and their causal relations from observations. In this setting, an important challenge is to model both lagged causal relations across observation intervals and faster causal effects that appear as instantaneous relations within an interval, while accounting for nonstationarity in time-series data. However, methods that jointly handle these causal relations and nonstationarity remain limited. To address this gap, we establish sufficient conditions for identifying latent states up to component permutation and component-wise invertible transformations, and their instantaneous and lagged causal structures up to the same permutation, using an observed auxiliary variable, such as time or a condition label, associated with changes in transition-noise distributions. Based on these results, we propose iCReN, a framework that uses contrastive learning with discrete or continuous auxiliary variables to learn latent representations and estimate their instantaneous and lagged causal structures. Experiments demonstrate accurate recovery of latent states and both instantaneous and lagged causal structures on synthetic data and the utility of the learned representations for downstream forecasting on real-world data.