# Interventional Causal Representation Learning

arXiv: https://arxiv.org/abs/2209.11924 · HTML: https://mlsanity.com/paper/2209.11924/

## Key facts

- Cited by 142 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 55 references that are in the map.
- First posted on arXiv 24 Sep 2022.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [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)
- [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)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [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)
- [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)
- [Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series](https://mlsanity.com/paper/2006.12107/) (2020)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [Desiderata for Representation Learning: A Causal Perspective](https://mlsanity.com/paper/2109.03795/) (2021)
- [Weakly Supervised Representation Learning with Sparse Perturbations](https://mlsanity.com/paper/2206.01101/) (2022)
- [Properties from Mechanisms: An Equivariance Perspective on Identifiable Representation Learning](https://mlsanity.com/paper/2110.15796/) (2021)
- [Cyclic Causal Discovery from Continuous Equilibrium Data](https://mlsanity.com/paper/1309.6849/) (2013)
- [Quantifying the Reality Gap in Robotic Manipulation Tasks](https://mlsanity.com/paper/1811.01484/) (2018)
- [Towards efficient representation identification in supervised learning](https://mlsanity.com/paper/2204.04606/) (2022)
- [Learning Latent Causal Dynamics](https://mlsanity.com/paper/2202.04828/) (2022)

## Built on by (most cited first, 30 of 142)

- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [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)
- [Multi-View Causal Representation Learning with Partial Observability](https://mlsanity.com/paper/2311.04056/) (2023)
- [Causal Representation Learning from Multiple Distributions: A General Setting](https://mlsanity.com/paper/2402.05052/) (2024)
- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
- [Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolation](https://mlsanity.com/paper/2307.02598/) (2023)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [Score-based Causal Representation Learning with Interventions](https://mlsanity.com/paper/2301.08230/) (2023)
- [A Sparsity Principle for Partially Observable Causal Representation Learning](https://mlsanity.com/paper/2403.08335/) (2024)
- [Learning nonparametric latent causal graphs with unknown interventions](https://mlsanity.com/paper/2306.02899/) (2023)
- [General Identifiability and Achievability for Causal Representation Learning](https://mlsanity.com/paper/2310.15450/) (2023)
- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [Causal Representation Learning Made Identifiable by Grouping of Observational Variables](https://mlsanity.com/paper/2310.15709/) (2023)
- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [Unifying Causal Representation Learning with the Invariance Principle](https://mlsanity.com/paper/2409.02772/) (2024)
- [When Does LeJEPA Learn a World Model?](https://mlsanity.com/paper/2605.26379/) (2026)
- [Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Models](https://mlsanity.com/paper/2402.09236/) (2024)
- [Multi-Domain Causal Representation Learning via Weak Distributional Invariances](https://mlsanity.com/paper/2310.02854/) (2023)
- [Identifiable Latent Polynomial Causal Models Through the Lens of Change](https://mlsanity.com/paper/2310.15580/) (2023)
- [Marrying Causal Representation Learning with Dynamical Systems for Science](https://mlsanity.com/paper/2405.13888/) (2024)
- [Causal Triplet: An Open Challenge for Intervention-centric Causal Representation Learning](https://mlsanity.com/paper/2301.05169/) (2023)
- [From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modeling](https://mlsanity.com/paper/2310.11011/) (2023)
- [Identifying Representations for Intervention Extrapolation](https://mlsanity.com/paper/2310.04295/) (2023)
- [Object-centric architectures enable efficient causal representation learning](https://mlsanity.com/paper/2310.19054/) (2023)
- [Interaction Asymmetry: A General Principle for Learning Composable Abstractions](https://mlsanity.com/paper/2411.07784/) (2024)
- [Identifying Linearly-Mixed Causal Representations from Multi-Node Interventions](https://mlsanity.com/paper/2311.02695/) (2023)
- [Learning Causally Disentangled Representations via the Principle of Independent Causal Mechanisms](https://mlsanity.com/paper/2306.01213/) (2023)
- [Linear Causal Representation Learning from Unknown Multi-node Interventions](https://mlsanity.com/paper/2406.05937/) (2024)

## Abstract (arXiv)

Causal representation learning seeks to extract high-level latent factors from low-level sensory data. Most existing methods rely on observational data and structural assumptions (e.g., conditional independence) to identify the latent factors. However, interventional data is prevalent across applications. Can interventional data facilitate causal representation learning? We explore this question in this paper. The key observation is that interventional data often carries geometric signatures of the latent factors' support (i.e. what values each latent can possibly take). For example, when the latent factors are causally connected, interventions can break the dependency between the intervened latents' support and their ancestors'. Leveraging this fact, we prove that the latent causal factors can be identified up to permutation and scaling given data from perfect do interventions. Moreover, we can achieve block affine identification, namely the estimated latent factors are only entangled with a few other latents if we have access to data from imperfect interventions. These results highlight the unique power of interventional data in causal representation learning; they can enable provable identification of latent factors without any assumptions about their distributions or dependency structure.