# Learning Causal Abstractions of Linear Structural Causal Models

arXiv: https://arxiv.org/abs/2406.00394 · HTML: https://mlsanity.com/paper/2406.00394/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 23 references that are in the map.
- First posted on arXiv 1 Jun 2024.

## Builds on (most cited first, 14 of 14)

- [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)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Interpretability at Scale: Identifying Causal Mechanisms in Alpaca](https://mlsanity.com/paper/2305.08809/) (2023)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions](https://mlsanity.com/paper/2301.05893/) (2023)
- [Foundations of Causal Discovery on Groups of Variables](https://mlsanity.com/paper/2306.07047/) (2023)
- [Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learning](https://mlsanity.com/paper/2309.07742/) (2023)
- [Unsupervised Discovery of El Nino Using Causal Feature Learning on Microlevel Climate Data](https://mlsanity.com/paper/1605.09370/) (2016)
- [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)
- [Causal Optimal Transport of Abstractions](https://mlsanity.com/paper/2312.08107/) (2023)
- [Clustering and Structural Robustness in Causal Diagrams](https://mlsanity.com/paper/2111.04513/) (2021)

## Built on by (most cited first, 11 of 11)

- [Causal Abstraction Learning based on the Semantic Embedding Principle](https://mlsanity.com/paper/2502.00407/) (2025)
- [Aligning Graphical and Functional Causal Abstractions](https://mlsanity.com/paper/2412.17080/) (2024)
- [Coarsening Causal DAG Models](https://mlsanity.com/paper/2601.10531/) (2026)
- [Structural Causal Bottleneck Models](https://mlsanity.com/paper/2603.08682/) (2026)
- [Distributionally Robust Causal Abstractions](https://mlsanity.com/paper/2510.04842/) (2025)
- [Cluster-Dags as Powerful Background Knowledge For Causal Discovery](https://mlsanity.com/paper/2512.10032/) (2025)
- [Learning Consistent Causal Abstraction Networks](https://mlsanity.com/paper/2602.02623/) (2026)
- [Unsupervised Causal Abstractions Discovery](https://mlsanity.com/paper/2606.19594/) (2026)
- [Multi-Level Causal Embeddings](https://mlsanity.com/paper/2602.22287/) (2026)
- [Invariance of Clustering Operations in Causal Effect Identification](https://mlsanity.com/paper/2610.03101/) (2026)
- [GO-Based Clustering for Learning Cluster-Level Causal Gene Regulatory Networks](https://mlsanity.com/paper/2610.06042/) (2026)

## Abstract (arXiv)

The need for modelling causal knowledge at different levels of granularity arises in several settings. Causal Abstraction provides a framework for formalizing this problem by relating two Structural Causal Models at different levels of detail. Despite increasing interest in applying causal abstraction, e.g. in the interpretability of large machine learning models, the graphical and parametrical conditions under which a causal model can abstract another are not known. Furthermore, learning causal abstractions from data is still an open problem. In this work, we tackle both issues for linear causal models with linear abstraction functions. First, we characterize how the low-level coefficients and the abstraction function determine the high-level coefficients and how the high-level model constrains the causal ordering of low-level variables. Then, we apply our theoretical results to learn high-level and low-level causal models and their abstraction function from observational data. In particular, we introduce Abs-LiNGAM, a method that leverages the constraints induced by the learned high-level model and the abstraction function to speedup the recovery of the larger low-level model, under the assumption of non-Gaussian noise terms. In simulated settings, we show the effectiveness of learning causal abstractions from data and the potential of our method in improving scalability of causal discovery.