# What is causal about causal models and representations?

arXiv: https://arxiv.org/abs/2501.19335 · HTML: https://mlsanity.com/paper/2501.19335/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 99 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 30 of 52)

- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [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)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Inducing Causal Structure for Interpretable Neural Networks](https://mlsanity.com/paper/2112.00826/) (2021)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [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)
- [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)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Identifiability Results for Multimodal Contrastive Learning](https://mlsanity.com/paper/2303.09166/) (2023)
- [Visual Causal Feature Learning](https://mlsanity.com/paper/1412.2309/) (2014)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [The Use and Misuse of Counterfactuals in Ethical Machine Learning](https://mlsanity.com/paper/2102.05085/) (2021)
- [Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learning](https://mlsanity.com/paper/2211.14666/) (2022)
- [What's Sex Got To Do With Fair Machine Learning?](https://mlsanity.com/paper/2006.01770/) (2020)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [A Sparsity Principle for Partially Observable Causal Representation Learning](https://mlsanity.com/paper/2403.08335/) (2024)
- [General Identifiability and Achievability for Causal Representation Learning](https://mlsanity.com/paper/2310.15450/) (2023)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [Properties from Mechanisms: An Equivariance Perspective on Identifiable Representation Learning](https://mlsanity.com/paper/2110.15796/) (2021)
- [Causal Abstraction with Soft Interventions](https://mlsanity.com/paper/2211.12270/) (2022)

## Built on by (most cited first, 6 of 6)

- [The Non-Linear Representation Dilemma: Is Causal Abstraction Enough for Mechanistic Interpretability?](https://mlsanity.com/paper/2507.08802/) (2025)
- [Embracing Discrete Search: A Reasonable Approach to Causal Structure Learning](https://mlsanity.com/paper/2510.04970/) (2025)
- [Structural Causal Bottleneck Models](https://mlsanity.com/paper/2603.08682/) (2026)
- [How PC-based Methods Err: Towards Better Reporting of Assumption Violations and Small Sample Errors](https://mlsanity.com/paper/2502.14719/) (2025)
- [Linear Causal Representation Learning by Topological Ordering, Pruning, and Disentanglement](https://mlsanity.com/paper/2509.22553/) (2025)
- [Causal Foundations of Collective Agency](https://mlsanity.com/paper/2605.00248/) (2026)

## Abstract (arXiv)

Causal Bayesian networks are 'causal' models since they make predictions about interventional distributions. To connect such causal model predictions to real-world outcomes, we must determine which actions in the world correspond to which interventions in the model. For example, to interpret an action as an intervention on a treatment variable, the action will presumably have to a) change the distribution of treatment in a way that corresponds to the intervention, and b) not change other aspects, such as how the outcome depends on the treatment; while the marginal distributions of some variables may change as an effect. We introduce a formal framework to make such requirements for different interpretations of actions as interventions precise. We prove that the seemingly natural interpretation of actions as interventions is circular: Under this interpretation, every causal Bayesian network that correctly models the observational distribution is trivially also interventionally valid, and no action yields empirical data that could possibly falsify such a model. We prove an impossibility result: No interpretation exists that is non-circular and simultaneously satisfies a set of natural desiderata. Instead, we examine non-circular interpretations that may violate some desiderata and show how this may in turn enable the falsification of causal models. By rigorously examining how a causal Bayesian network could be a 'causal' model of the world instead of merely a mathematical object, our formal framework contributes to the conceptual foundations of causal representation learning, causal discovery, and causal abstraction, while also highlighting some limitations of existing approaches.