Research map / Probabilistic and scientific modeling / Causal discovery
Causal Abstractions, Categorically Unified
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Proposes a categorical framework for causal abstraction, defining abstractions as deterministic natural transformations between Markov functors on free Markov categories of DAGs, and recovers several prior notions (CBN abstractions, tau-abstractions, phi-abstractions, ADMG do-calculus).
Problem
Existing causal abstraction notions (interventional consistency, tau-abstractions, phi-abstractions, mechanistic interpretability abstractions) are fragmented and lack a unified treatment covering non-aligned interventions, effect-based clustering, and confounded (ADMG) models.
Approach
Model causal models as Markov functors from free Markov categories generated by DAGs; define causal abstraction as a deterministic natural transformation together with an embedding of restricted free Markov categories, allowing lax monoidal functors for non-aligned interventions and a reversed (effect-focused) variant with deterministic left-inverses.
Key results
- Proves that for CBNs over Stoch, the categorical causal abstraction definition is equivalent to the interventional-distribution-consistency definition (necessity and sufficiency).
- Proves graphical abstractions of a DAG are exactly the DAGs whose restricted free Markov categories embed into those of the original DAG.
- Generalizes do-calculus transfer from clustered high-level ADMGs to low-level graphs to all graphical abstractions between ADMGs.
Surprising findings
- Phi-abstractions (graph-homomorphism based) cannot express simple node clusterings, such as merging a chain A->B->C into one node.
Limitations
- Framework is purely theoretical with no empirical validation.
- Cyclic causal models are not covered.
- Some results (e.g., proof generalization) are restricted to specific Markov categories such as Stoch and Set.
Experimental setup
Baselines: phi-abstraction framework constructive tau-abstraction strong tau-abstraction neural causal abstractions
Builds on: Markov categories causal abstraction (Rubenstein et al.) phi-abstractions (Otsuka and Saigo) do-calculus tau-abstractions
Closest papers by meaning
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- Causal Abstraction Learning based on the Semantic Embedding Principle (ICML 2025 · similarity 0.88)
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- A Fixed-Point Approach for Causal Generative Modeling (ICML 2024 · similarity 0.87)
- Characterization and Learning of Causal Graphs from Hard Interventions (NeurIPS 2025 · similarity 0.87)
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