# Targeted Reduction of Causal Models

arXiv: https://arxiv.org/abs/2311.18639 · HTML: https://mlsanity.com/paper/2311.18639/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 37 references that are in the map.
- First posted on arXiv 30 Nov 2023.

## Builds on (most cited first, 23 of 23)

- [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)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [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)
- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Causal structure based root cause analysis of outliers](https://mlsanity.com/paper/1912.02724/) (2019)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Visual Causal Feature Learning](https://mlsanity.com/paper/1412.2309/) (2014)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [Counterfactuals uncover the modular structure of deep generative models](https://mlsanity.com/paper/1812.03253/) (2018)
- [From Ordinary Differential Equations to Structural Causal Models: the deterministic case](https://mlsanity.com/paper/1408.2063/) (2014)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [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)
- [Unsupervised Discovery of El Nino Using Causal Feature Learning on Microlevel Climate Data](https://mlsanity.com/paper/1605.09370/) (2016)
- [Backtracking Counterfactuals](https://mlsanity.com/paper/2211.00472/) (2022)
- [Learning Game-Theoretic Models of Multiagent Trajectories Using Implicit Layers](https://mlsanity.com/paper/2008.07303/) (2020)
- [Meaningful Causal Aggregation and Paradoxical Confounding](https://mlsanity.com/paper/2304.11625/) (2023)
- [Learning soft interventions in complex equilibrium systems](https://mlsanity.com/paper/2112.05729/) (2021)

## Built on by (most cited first, 15 of 15)

- [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)
- [Aligning Graphical and Functional Causal Abstractions](https://mlsanity.com/paper/2412.17080/) (2024)
- [What is causal about causal models and representations?](https://mlsanity.com/paper/2501.19335/) (2025)
- [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)
- [Distributionally Robust Causal Abstractions](https://mlsanity.com/paper/2510.04842/) (2025)
- [Systems with Switching Causal Relations: A Meta-Causal Perspective](https://mlsanity.com/paper/2410.13054/) (2024)
- [Causal Representation Learning for Generalisable Recommendation](https://mlsanity.com/paper/2605.27043/) (2026)
- [Linear causal disentanglement via higher-order cumulants](https://mlsanity.com/paper/2407.04605/) (2024)
- [Learning Nonlinear Causal Reductions to Explain Reinforcement Learning Policies](https://mlsanity.com/paper/2507.14901/) (2025)
- [Unsupervised Causal Abstractions Discovery](https://mlsanity.com/paper/2606.19594/) (2026)
- [Causal Learning in Biomedical Applications: Krebs Cycle as a Benchmark](https://mlsanity.com/paper/2406.15189/) (2024)
- [Learning Joint Interventional Effects from Single-Variable Interventions in Additive Models](https://mlsanity.com/paper/2506.04945/) (2025)
- [Validating Causal Abstraction Metrics on Simulated Complex Systems](https://mlsanity.com/paper/2607.00267/) (2026)

## Abstract (arXiv)

Why does a phenomenon occur? Addressing this question is central to most scientific inquiries and often relies on simulations of scientific models. As models become more intricate, deciphering the causes behind phenomena in high-dimensional spaces of interconnected variables becomes increasingly challenging. Causal Representation Learning (CRL) offers a promising avenue to uncover interpretable causal patterns within these simulations through an interventional lens. However, developing general CRL frameworks suitable for practical applications remains an open challenge. We introduce Targeted Causal Reduction (TCR), a method for condensing complex intervenable models into a concise set of causal factors that explain a specific target phenomenon. We propose an information theoretic objective to learn TCR from interventional data of simulations, establish identifiability for continuous variables under shift interventions and present a practical algorithm for learning TCRs. Its ability to generate interpretable high-level explanations from complex models is demonstrated on toy and mechanical systems, illustrating its potential to assist scientists in the study of complex phenomena in a broad range of disciplines.