# General Identifiability and Achievability for Causal Representation Learning

arXiv: https://arxiv.org/abs/2310.15450 · HTML: https://mlsanity.com/paper/2310.15450/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 48 references that are in the map.
- First posted on arXiv 24 Oct 2023.

## Builds on (most cited first, 28 of 28)

- [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)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Learning Linear Causal Representations from Interventions under General Nonlinear Mixing](https://mlsanity.com/paper/2306.02235/) (2023)
- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Identifiability Guarantees for Causal Disentanglement from Soft Interventions](https://mlsanity.com/paper/2307.06250/) (2023)
- [Weakly Supervised Disentanglement with Guarantees](https://mlsanity.com/paper/1910.09772/) (2019)
- [Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series](https://mlsanity.com/paper/2006.12107/) (2020)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [Weakly Supervised Representation Learning with Sparse Perturbations](https://mlsanity.com/paper/2206.01101/) (2022)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems](https://mlsanity.com/paper/2206.06169/) (2022)
- [Score-based Causal Representation Learning with Interventions](https://mlsanity.com/paper/2301.08230/) (2023)
- [Scalable Causal Discovery with Score Matching](https://mlsanity.com/paper/2304.03382/) (2023)
- [On Implicit Regularization in β-VAEs](https://mlsanity.com/paper/2002.00041/) (2020)
- [Identifying Weight-Variant Latent Causal Models](https://mlsanity.com/paper/2208.14153/) (2022)
- [Learning nonparametric latent causal graphs with unknown interventions](https://mlsanity.com/paper/2306.02899/) (2023)
- [Properties from Mechanisms: An Equivariance Perspective on Identifiable Representation Learning](https://mlsanity.com/paper/2110.15796/) (2021)

## Built on by (most cited first, 30 of 34)

- [Unifying Causal Representation Learning with the Invariance Principle](https://mlsanity.com/paper/2409.02772/) (2024)
- [Marrying Causal Representation Learning with Dynamical Systems for Science](https://mlsanity.com/paper/2405.13888/) (2024)
- [Interaction Asymmetry: A General Principle for Learning Composable Abstractions](https://mlsanity.com/paper/2411.07784/) (2024)
- [Learning Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity](https://mlsanity.com/paper/2311.12267/) (2023)
- [Linear Causal Representation Learning from Unknown Multi-node Interventions](https://mlsanity.com/paper/2406.05937/) (2024)
- [All or None: Identifiable Linear Properties of Next-token Predictors in Language Modeling](https://mlsanity.com/paper/2410.23501/) (2024)
- [Towards Interpretable Deep Generative Models via Causal Representation Learning](https://mlsanity.com/paper/2504.11609/) (2025)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [Prediction-Powered Causal Inferences](https://mlsanity.com/paper/2502.06343/) (2025)
- [On the Identifiability of Controlled World Models](https://mlsanity.com/paper/2607.22430/) (2026)
- [Identifiability Guarantees for Causal Disentanglement from Purely Observational Data](https://mlsanity.com/paper/2410.23620/) (2024)
- [What is causal about causal models and representations?](https://mlsanity.com/paper/2501.19335/) (2025)
- [Towards Identifiable Latent Additive Noise Models](https://mlsanity.com/paper/2403.15711/) (2024)
- [Identifying General Mechanism Shifts in Linear Causal Representations](https://mlsanity.com/paper/2410.24059/) (2024)
- [The Third Pillar of Causal Analysis? A Measurement Perspective on Causal Representations](https://mlsanity.com/paper/2505.17708/) (2025)
- [When Does Closeness in Distribution Imply Representational Similarity? An Identifiability Perspective](https://mlsanity.com/paper/2506.03784/) (2025)
- [Exploratory Causal Inference in SAEnce](https://mlsanity.com/paper/2510.14073/) (2025)
- [Contextures: Representations from Contexts](https://mlsanity.com/paper/2505.01557/) (2025)
- [From Pixels to Factors: Learning Independently Controllable State Variables for Reinforcement Learning](https://mlsanity.com/paper/2510.02484/) (2025)
- [Linear causal disentanglement via higher-order cumulants](https://mlsanity.com/paper/2407.04605/) (2024)
- [Identifiable Representation and Model Learning for Latent Dynamic Systems](https://mlsanity.com/paper/2410.17882/) (2024)
- [Intervening to Learn and Compose Causally Disentangled Representations](https://mlsanity.com/paper/2507.04754/) (2025)
- [Multi-Domain Empirical Bayes for Linearly-Mixed Causal Representations](https://mlsanity.com/paper/2603.18404/) (2026)
- [Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation](https://mlsanity.com/paper/2606.18509/) (2026)
- [Catastrophic Compositional Generation: Why Vanilla Diffusion Models Fail to Extrapolate](https://mlsanity.com/paper/2606.23920/) (2026)
- [A Generative Framework for Causal Estimation via Importance-Weighted Diffusion Distillation](https://mlsanity.com/paper/2505.11444/) (2025)
- [Learning Joint Interventional Effects from Single-Variable Interventions in Additive Models](https://mlsanity.com/paper/2506.04945/) (2025)
- [Incorporating Interventional Independence Improves Robustness against Interventional Distribution Shift](https://mlsanity.com/paper/2507.05412/) (2025)
- [Linear Causal Representation Learning by Topological Ordering, Pruning, and Disentanglement](https://mlsanity.com/paper/2509.22553/) (2025)
- [ROPES: Robotic Pose Estimation via Score-Based Causal Representation Learning](https://mlsanity.com/paper/2510.20884/) (2025)

## Abstract (arXiv)

This paper focuses on causal representation learning (CRL) under a general nonparametric latent causal model and a general transformation model that maps the latent data to the observational data. It establishes identifiability and achievability results using two hard uncoupled interventions per node in the latent causal graph. Notably, one does not know which pair of intervention environments have the same node intervened (hence, uncoupled). For identifiability, the paper establishes that perfect recovery of the latent causal model and variables is guaranteed under uncoupled interventions. For achievability, an algorithm is designed that uses observational and interventional data and recovers the latent causal model and variables with provable guarantees. This algorithm leverages score variations across different environments to estimate the inverse of the transformer and, subsequently, the latent variables. The analysis, additionally, recovers the identifiability result for two hard coupled interventions, that is when metadata about the pair of environments that have the same node intervened is known. This paper also shows that when observational data is available, additional faithfulness assumptions that are adopted by the existing literature are unnecessary.