Approximate Causal Abstraction
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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.
Key facts. Cited by 62 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Jun 2019.
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Citing papers per year: 2021: 5; 2022: 10; 2023: 17; 2024: 12; 2025: 12; 2026: 6.
62 papers.
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- 2021Causal Abstractions of Neural Networkscited by 401
- 2023Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representationscited by 197
- 2023Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretabilitycited by 194
- 2023Localizing Model Behavior with Path Patchingcited by 182
- 2021Inducing Causal Structure for Interpretable Neural Networkscited by 107
- 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
- 2023Interpretability at Scale: Identifying Causal Mechanisms in Alpacacited by 102
- 2024RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representationscited by 77
- 2021Local Explanations via Necessity and Sufficiency: Unifying Theory and Practicecited by 45
- 2021Compositional Abstraction Error and a Category of Causal Modelscited by 32
- 2024Mechanistic?cited by 25
- 2022Causal Abstraction with Soft Interventionscited by 23
38 more
- 2022Causal Inference Through the Structural Causal Marginal Problemcited by 22
- 2023Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learningcited by 22
- 2023Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributionscited by 21
- 2021Causal Distillation for Language Modelscited by 19
- 2024A Philosophical Introduction to Language Models - Part II: The Way Forwardcited by 17
- 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applicationscited by 17
- 2022Inducing Character-level Structure in Subword-based Language Models with Type-level Interchange Intervention Trainingcited by 16
- 2023Targeted Reduction of Causal Modelscited by 15
- 2022Abstraction between Structural Causal Models: A Review of Definitions and Propertiescited by 14
- 2022On the Equivalence of Causal Models: A Category-Theoretic Approachcited by 13
- 2023Causal Optimal Transport of Abstractionscited by 13
- 2024Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environmentcited by 12
- 2023Comparing Causal Frameworks: Potential Outcomes, Structural Models, Graphs, and Abstractionscited by 11
- 2022Towards a Grounded Theory of Causation for Embodied AIcited by 9
- 2023A Measure-Theoretic Axiomatisation of Causalitycited by 8
- 2022FACT: Learning Governing Abstractions Behind Integer Sequencescited by 6
- 2023Quantifying Consistency and Information Loss for Causal Abstraction Learningcited by 6
- 2023Interventionally Consistent Surrogates for Agent-based Simulatorscited by 6
- 2025What is causal about causal models and representations?cited by 6
- 2025Sample-efficient Learning of Concepts with Theoretical Guarantees: from Data to Concepts without Interventionscited by 6
- 2023Meaningful Causal Aggregation and Paradoxical Confoundingcited by 5
- 2024Causally Abstracted Multi-armed Banditscited by 5
- 2024Causal Representation Learning in Temporal Data via Single-Parent Decodingcited by 5
- 2024The Causal Information Bottleneck and Optimal Causal Variable Abstractionscited by 4
- 2025Combining Causal Models for More Accurate Abstractions of Neural Networkscited by 4
- 2022Neural Information Squeezer for Causal Emergencecited by 3
- 2022Towards Computing an Optimal Abstraction for Structural Causal Modelscited by 3
- 2022Language Models Understand Us, Poorlycited by 3
- 2023Causal Entropy and Information Gain for Measuring Causal Controlcited by 3
- 2023Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studiescited by 3
- 2025Distributionally Robust Causal Abstractionscited by 3
- 2024Toward A Causal Framework for Modeling Perceptioncited by 2
- 2024Causal Abstraction in Model Interpretability: A Compact Surveycited by 2
- 2025Modeling Discrimination with Causal Abstractioncited by 2
- 2026Coarsening Causal DAG Modelscited by 2
- 2023Do Not Marginalize Mechanisms, Rather Consolidate!cited by 1
- 2024Intuitions of Compromise: Utilitarianism vs. Contractualismcited by 1
- 2024Factored space models: Towards causality between levels of abstractioncited by 1
50 most cited of 62 All 62 (JSON)
- 2026Score-Based Learning of Cluster DAGs from Interventions8 Oct 2026
- 2026Causal Foundations of Collective Agency30 Apr 2026
- 2026Causal Mechanism Reduction: Mechanism Replacement for Neural Network Pruning and Abstraction27 Feb 2026
- 2026Multi-Level Causal Embeddings25 Feb 2026
- 2026Rethinking Chronological Causal Discovery with Signal Processing23 Feb 2026
- 2026Coarsening Causal DAG Models15 Jan 2026
- 2025Causal Counterfactuals Reconsidered14 Dec 2025
- 2025Distributionally Robust Causal Abstractions6 Oct 2025
- 2025Heads or Tails: A Simple Example of Causal Abstractive Simulation1 Sep 2025
- 2025Learning Nonlinear Causal Reductions to Explain Reinforcement Learning Policies20 Jul 2025
- 2025Causality in the human niche: lessons for machine learning13 Jun 2025
- 2025Causal Feature Learning in the Social Sciences17 Mar 2025
38 more
- 2025Combining Causal Models for More Accurate Abstractions of Neural Networks14 Mar 2025
- 2025Addressing pitfalls in implicit unobserved confounding synthesis using explicit block hierarchical ancestral sampling12 Mar 2025
- 2025An Algebraic Framework for Hierarchical Probabilistic Abstraction28 Feb 2025
- 2025Sample-efficient Learning of Concepts with Theoretical Guarantees: from Data to Concepts without Interventions10 Feb 2025
- 2025What is causal about causal models and representations?31 Jan 2025
- 2025Modeling Discrimination with Causal Abstraction14 Jan 2025
- 2024Factored space models: Towards causality between levels of abstraction3 Dec 2024
- 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications2 Dec 2024
- 2024Causal Abstraction in Model Interpretability: A Compact Survey26 Oct 2024
- 2024Causal Representation Learning in Temporal Data via Single-Parent Decoding9 Oct 2024
- 2024Mechanistic?7 Oct 2024
- 2024Intuitions of Compromise: Utilitarianism vs. Contractualism7 Oct 2024
- 2024The Causal Information Bottleneck and Optimal Causal Variable Abstractions1 Oct 2024
- 2024Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment19 Jun 2024
- 2024A Philosophical Introduction to Language Models - Part II: The Way Forward6 May 2024
- 2024Causally Abstracted Multi-armed Bandits26 Apr 2024
- 2024RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations27 Feb 2024
- 2024Toward A Causal Framework for Modeling Perception24 Jan 2024
- 2023Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies28 Dec 2023
- 2023Interventionally Consistent Surrogates for Agent-based Simulators18 Dec 2023
- 2023Causal Optimal Transport of Abstractions13 Dec 2023
- 2023Targeted Reduction of Causal Models30 Nov 2023
- 2023Do Not Marginalize Mechanisms, Rather Consolidate!12 Oct 2023
- 2023Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learning14 Sep 2023
- 2023Causal Entropy and Information Gain for Measuring Causal Control14 Sep 2023
- 2023Comparing Causal Frameworks: Potential Outcomes, Structural Models, Graphs, and Abstractions25 Jun 2023
- 2023Nonparametric Identifiability of Causal Representations from Unknown Interventions1 Jun 2023
- 2023A Measure-Theoretic Axiomatisation of Causality19 May 2023
- 2023Interpretability at Scale: Identifying Causal Mechanisms in Alpaca15 May 2023
- 2023Quantifying Consistency and Information Loss for Causal Abstraction Learning7 May 2023
- 2023Meaningful Causal Aggregation and Paradoxical Confounding23 Apr 2023
- 2023Localizing Model Behavior with Path Patching12 Apr 2023
- 2023Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations5 Mar 2023
- 2023Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions14 Jan 2023
- 2023Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability11 Jan 2023
- 2022Inducing Character-level Structure in Subword-based Language Models with Type-level Interchange Intervention Training19 Dec 2022
- 2022Causal Abstraction with Soft Interventions22 Nov 2022
- 2022Language Models Understand Us, Poorly19 Oct 2022
50 newest of 62 All 62 (JSON)
- 2021Causal Abstractions of Neural Networkscited by 401
- 2023Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representationscited by 197
- 2023Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretabilitycited by 194
- 2023Localizing Model Behavior with Path Patchingcited by 182
- 2021Inducing Causal Structure for Interpretable Neural Networkscited by 107
- 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
- 2023Interpretability at Scale: Identifying Causal Mechanisms in Alpacacited by 102
- 2024RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representationscited by 77
- 2021Local Explanations via Necessity and Sufficiency: Unifying Theory and Practicecited by 45
- 2021Compositional Abstraction Error and a Category of Causal Modelscited by 32
- 2024Mechanistic?cited by 25
- 2022Causal Abstraction with Soft Interventionscited by 23
12 most cited of 62 All 62 (JSON)
- 2026Score-Based Learning of Cluster DAGs from Interventions8 Oct 2026
- 2026Causal Foundations of Collective Agency30 Apr 2026
- 2026Causal Mechanism Reduction: Mechanism Replacement for Neural Network Pruning and Abstraction27 Feb 2026
- 2026Multi-Level Causal Embeddings25 Feb 2026
- 2026Rethinking Chronological Causal Discovery with Signal Processing23 Feb 2026
- 2026Coarsening Causal DAG Models15 Jan 2026
- 2025Causal Counterfactuals Reconsidered14 Dec 2025
- 2025Distributionally Robust Causal Abstractions6 Oct 2025
- 2025Heads or Tails: A Simple Example of Causal Abstractive Simulation1 Sep 2025
- 2025Learning Nonlinear Causal Reductions to Explain Reinforcement Learning Policies20 Jul 2025
- 2025Causality in the human niche: lessons for machine learning13 Jun 2025
- 2025Causal Feature Learning in the Social Sciences17 Mar 2025
12 newest of 62 All 62 (JSON)