# Approximate Causal Abstraction

arXiv: https://arxiv.org/abs/1906.11583 · HTML: https://mlsanity.com/paper/1906.11583/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2019.

## Built on by (most cited first, 30 of 63)

- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (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)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [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)
- [RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations](https://mlsanity.com/paper/2402.17700/) (2024)
- [Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice](https://mlsanity.com/paper/2103.14651/) (2021)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [Mechanistic?](https://mlsanity.com/paper/2410.09087/) (2024)
- [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)
- [Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learning](https://mlsanity.com/paper/2309.07742/) (2023)
- [Causal Distillation for Language Models](https://mlsanity.com/paper/2112.02505/) (2021)
- [A Philosophical Introduction to Language Models - Part II: The Way Forward](https://mlsanity.com/paper/2405.03207/) (2024)
- [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)
- [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)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [Comparing Causal Frameworks: Potential Outcomes, Structural Models, Graphs, and Abstractions](https://mlsanity.com/paper/2306.14351/) (2023)
- [Towards a Grounded Theory of Causation for Embodied AI](https://mlsanity.com/paper/2206.13973/) (2022)
- [A Measure-Theoretic Axiomatisation of Causality](https://mlsanity.com/paper/2305.17139/) (2023)
- [Quantifying Consistency and Information Loss for Causal Abstraction Learning](https://mlsanity.com/paper/2305.04357/) (2023)
- [FACT: Learning Governing Abstractions Behind Integer Sequences](https://mlsanity.com/paper/2209.09543/) (2022)
- [Interventionally Consistent Surrogates for Agent-based Simulators](https://mlsanity.com/paper/2312.11158/) (2023)

## Abstract (arXiv)

Scientific models describe natural phenomena at different levels of abstraction. Abstract descriptions can provide the basis for interventions on the system and explanation of observed phenomena at a level of granularity that is coarser than the most fundamental account of the system. Beckers and Halpern (2019), building on work of Rubenstein et al. (2017), developed an account of abstraction for causal models that is exact. Here we extend this account to the more realistic case where an abstract causal model offers only an approximation of the underlying system. We show how the resulting account handles the discrepancy that can arise between low- and high-level causal models of the same system, and in the process provide an account of how one causal model approximates another, a topic of independent interest. Finally, we extend the account of approximate abstractions to probabilistic causal models, indicating how and where uncertainty can enter into an approximate abstraction.