# Abstracting Causal Models

arXiv: https://arxiv.org/abs/1812.03789 · HTML: https://mlsanity.com/paper/1812.03789/

## Key facts

- Cited by 107 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2018.

## Built on by (most cited first, 30 of 107)

- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [Inducing Causal Structure for Interpretable Neural Networks](https://mlsanity.com/paper/2112.00826/) (2021)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Interpretability at Scale: Identifying Causal Mechanisms in Alpaca](https://mlsanity.com/paper/2305.08809/) (2023)
- [The Non-Linear Representation Dilemma: Is Causal Abstraction Enough for Mechanistic Interpretability?](https://mlsanity.com/paper/2507.08802/) (2025)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [Everything, Everywhere, All at Once: Is Mechanistic Interpretability Identifiable?](https://mlsanity.com/paper/2502.20914/) (2025)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [Unifying Causal Representation Learning with the Invariance Principle](https://mlsanity.com/paper/2409.02772/) (2024)
- [Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior](https://mlsanity.com/paper/2605.05115/) (2026)
- [Causal Inference Through the Structural Causal Marginal Problem](https://mlsanity.com/paper/2202.01300/) (2022)
- [Causal Abstraction with Soft Interventions](https://mlsanity.com/paper/2211.12270/) (2022)
- [Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions](https://mlsanity.com/paper/2301.05893/) (2023)
- [Interventional Sum-Product Networks: Causal Inference with Tractable Probabilistic Models](https://mlsanity.com/paper/2102.10440/) (2021)
- [Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learning](https://mlsanity.com/paper/2309.07742/) (2023)
- [Neural Causal Abstractions](https://mlsanity.com/paper/2401.02602/) (2024)
- [Causal Distillation for Language Models](https://mlsanity.com/paper/2112.02505/) (2021)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Inducing Character-level Structure in Subword-based Language Models with Type-level Interchange Intervention Training](https://mlsanity.com/paper/2212.09897/) (2022)
- [Abstraction between Structural Causal Models: A Review of Definitions and Properties](https://mlsanity.com/paper/2207.08603/) (2022)
- [A Causal Analysis of Harm](https://mlsanity.com/paper/2210.05327/) (2022)
- [Targeted Reduction of Causal Models](https://mlsanity.com/paper/2311.18639/) (2023)
- [On the Equivalence of Causal Models: A Category-Theoretic Approach](https://mlsanity.com/paper/2201.06981/) (2022)
- [Causal Optimal Transport of Abstractions](https://mlsanity.com/paper/2312.08107/) (2023)
- [The Dead Salmons of AI Interpretability](https://mlsanity.com/paper/2512.18792/) (2025)
- [Learning Causal Abstractions of Linear Structural Causal Models](https://mlsanity.com/paper/2406.00394/) (2024)
- [Position: An Inner Interpretability Framework for AI Inspired by Lessons from Cognitive Neuroscience](https://mlsanity.com/paper/2406.01352/) (2024)
- [How Causal Abstraction Underpins Computational Explanation](https://mlsanity.com/paper/2508.11214/) (2025)

## Abstract (arXiv)

We consider a sequence of successively more restrictive definitions of abstraction for causal models, starting with a notion introduced by Rubenstein et al. (2017) called exact transformation that applies to probabilistic causal models, moving to a notion of uniform transformation that applies to deterministic causal models and does not allow differences to be hidden by the "right" choice of distribution, and then to abstraction, where the interventions of interest are determined by the map from low-level states to high-level states, and strong abstraction, which takes more seriously all potential interventions in a model, not just the allowed interventions. We show that procedures for combining micro-variables into macro-variables are instances of our notion of strong abstraction, as are all the examples considered by Rubenstein et al.