# Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions

arXiv: https://arxiv.org/abs/2301.05893 · HTML: https://mlsanity.com/paper/2301.05893/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 14 Jan 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Abstraction and Analogy-Making in Artificial Intelligence](https://mlsanity.com/paper/2102.10717/) (2021)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics](https://mlsanity.com/paper/1908.07021/) (2019)
- [Understanding the role of importance weighting for deep learning](https://mlsanity.com/paper/2103.15209/) (2021)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [The Hamming Ball Sampler](https://mlsanity.com/paper/1504.08133/) (2015)
- [Abstraction between Structural Causal Models: A Review of Definitions and Properties](https://mlsanity.com/paper/2207.08603/) (2022)
- [On the Equivalence of Causal Models: A Category-Theoretic Approach](https://mlsanity.com/paper/2201.06981/) (2022)
- [Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC](https://mlsanity.com/paper/2102.02374/) (2021)
- [Towards Computing an Optimal Abstraction for Structural Causal Models](https://mlsanity.com/paper/2208.00894/) (2022)

## Built on by (most cited first, 23 of 23)

- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Targeted Reduction of Causal Models](https://mlsanity.com/paper/2311.18639/) (2023)
- [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)
- [Learning Causal Abstractions of Linear Structural Causal Models](https://mlsanity.com/paper/2406.00394/) (2024)
- [Causal Abstraction Learning based on the Semantic Embedding Principle](https://mlsanity.com/paper/2502.00407/) (2025)
- [Quantifying Consistency and Information Loss for Causal Abstraction Learning](https://mlsanity.com/paper/2305.04357/) (2023)
- [Interventionally Consistent Surrogates for Agent-based Simulators](https://mlsanity.com/paper/2312.11158/) (2023)
- [Causally Abstracted Multi-armed Bandits](https://mlsanity.com/paper/2404.17493/) (2024)
- [Aligning Graphical and Functional Causal Abstractions](https://mlsanity.com/paper/2412.17080/) (2024)
- [The Causal Information Bottleneck and Optimal Causal Variable Abstractions](https://mlsanity.com/paper/2410.00535/) (2024)
- [Combining Causal Models for More Accurate Abstractions of Neural Networks](https://mlsanity.com/paper/2503.11429/) (2025)
- [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)
- [Causal Representation Learning for Generalisable Recommendation](https://mlsanity.com/paper/2605.27043/) (2026)
- [Do Not Marginalize Mechanisms, Rather Consolidate!](https://mlsanity.com/paper/2310.08377/) (2023)
- [Causal Counterfactuals Reconsidered](https://mlsanity.com/paper/2512.12804/) (2025)
- [Unsupervised Causal Abstractions Discovery](https://mlsanity.com/paper/2606.19594/) (2026)
- [Multi-Level Causal Embeddings](https://mlsanity.com/paper/2602.22287/) (2026)
- [Validating Causal Abstraction Metrics on Simulated Complex Systems](https://mlsanity.com/paper/2607.00267/) (2026)
- [GO-Based Clustering for Learning Cluster-Level Causal Gene Regulatory Networks](https://mlsanity.com/paper/2610.06042/) (2026)
- [When Do Learned Blocks Preserve Causal Meaning? Block Identifiability and Constructive Causal Abstractions](https://mlsanity.com/paper/2610.18155/) (2026)

## Abstract (arXiv)

An abstraction can be used to relate two structural causal models representing the same system at different levels of resolution. Learning abstractions which guarantee consistency with respect to interventional distributions would allow one to jointly reason about evidence across multiple levels of granularity while respecting the underlying cause-effect relationships. In this paper, we introduce a first framework for causal abstraction learning between SCMs based on the formalization of abstraction recently proposed by Rischel (2020). Based on that, we propose a differentiable programming solution that jointly solves a number of combinatorial sub-problems, and we study its performance and benefits against independent and sequential approaches on synthetic settings and on a challenging real-world problem related to electric vehicle battery manufacturing.