# Causal Abstraction with Soft Interventions

arXiv: https://arxiv.org/abs/2211.12270 · HTML: https://mlsanity.com/paper/2211.12270/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 24 references that are in the map.
- First posted on arXiv 22 Nov 2022.

## Builds on (most cited first, 10 of 10)

- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [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)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Visual Causal Feature Learning](https://mlsanity.com/paper/1412.2309/) (2014)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [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)

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

- [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)
- [The Hydra Effect: Emergent Self-repair in Language Model Computations](https://mlsanity.com/paper/2307.15771/) (2023)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Targeted Reduction of Causal Models](https://mlsanity.com/paper/2311.18639/) (2023)
- [Causal Optimal Transport of Abstractions](https://mlsanity.com/paper/2312.08107/) (2023)
- [I Predict Therefore I Am: Is Next Token Prediction Enough to Learn Human-Interpretable Concepts from Data?](https://mlsanity.com/paper/2503.08980/) (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)
- [Meaningful Causal Aggregation and Paradoxical Confounding](https://mlsanity.com/paper/2304.11625/) (2023)
- [Combining Causal Models for More Accurate Abstractions of Neural Networks](https://mlsanity.com/paper/2503.11429/) (2025)
- [Certified Interventional Fidelity: Anytime-Valid, Adaptive Evaluation of Causal Claims in Mechanistic Interpretability](https://mlsanity.com/paper/2607.08349/) (2026)
- [Causal Abstraction in Model Interpretability: A Compact Survey](https://mlsanity.com/paper/2410.20161/) (2024)
- [Hidden APIs in Language Models: Discovering Reusable Causal Interfaces from Forked Futures](https://mlsanity.com/paper/2607.27617/) (2026)
- [On the Identifiability of Causal Abstractions](https://mlsanity.com/paper/2503.10834/) (2025)
- [Learning Nonlinear Causal Reductions to Explain Reinforcement Learning Policies](https://mlsanity.com/paper/2507.14901/) (2025)
- [Causal Mechanism Reduction: Mechanism Replacement for Neural Network Pruning and Abstraction](https://mlsanity.com/paper/2602.24266/) (2026)
- [Cyclic Counterfactuals under Shift-Scale Interventions](https://mlsanity.com/paper/2510.25005/) (2025)
- [Concept Component Analysis: A Principled Approach for Concept Extraction in LLMs](https://mlsanity.com/paper/2601.20420/) (2026)
- [Causal Foundations of Collective Agency](https://mlsanity.com/paper/2605.00248/) (2026)
- [Operationalising Relative Causal Knowledge: Backbone Identifiability from Private Reports on a Shared Outcome](https://mlsanity.com/paper/2608.10664/) (2026)
- [Local Gains and Fixed-Assignment Set Losses in Shared Set Decoders](https://mlsanity.com/paper/2608.14717/) (2026)
- [Score-Based Learning of Cluster DAGs from Interventions](https://mlsanity.com/paper/2610.11947/) (2026)

## Abstract (arXiv)

Causal abstraction provides a theory describing how several causal models can represent the same system at different levels of detail. Existing theoretical proposals limit the analysis of abstract models to "hard" interventions fixing causal variables to be constant values. In this work, we extend causal abstraction to "soft" interventions, which assign possibly non-constant functions to variables without adding new causal connections. Specifically, (i) we generalize τ-abstraction from Beckers and Halpern (2019) to soft interventions, (ii) we propose a further definition of soft abstraction to ensure a unique map ω between soft interventions, and (iii) we prove that our constructive definition of soft abstraction guarantees the intervention map ω has a specific and necessary explicit form.