One Model to Rule Them All: Canonically Gluing Causal Models Along Shared Substructures

Markus Englberger, Devendra Singh Dhami
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:1474-1497, 2026.

Abstract

Causal {Bayesian} Networks (CBNs) provide a framework for reasoning about interventions, but analyzing complex systems often requires working with multiple overlapping models or hierarchical levels of granularity. We study how to canonically merge separate causal models that share a common substructure or abstract representation. We formalize this problem using category theory. We construct two distinct categories of causal models where morphisms are defined by maps that commute with interventions. Depending on whether these maps are injective or surjective, they represent causal submodels or causal abstractions, respectively. We demonstrate that the canonical merging of models sharing a common subsystem corresponds to computing a pushout in the category of submodels, while merging models sharing a common abstraction corresponds to a pullback in the category of abstractions. We establish sufficient topological and domain-level conditions under which these universal constructions exist.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-englberger26a, title = {One Model to Rule Them All: Canonically Gluing Causal Models Along Shared Substructures}, author = {Englberger, Markus and Dhami, Devendra Singh}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {1474--1497}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/englberger26a/englberger26a.pdf}, url = {https://proceedings.mlr.press/v337/englberger26a.html}, abstract = {Causal {Bayesian} Networks (CBNs) provide a framework for reasoning about interventions, but analyzing complex systems often requires working with multiple overlapping models or hierarchical levels of granularity. We study how to canonically merge separate causal models that share a common substructure or abstract representation. We formalize this problem using category theory. We construct two distinct categories of causal models where morphisms are defined by maps that commute with interventions. Depending on whether these maps are injective or surjective, they represent causal submodels or causal abstractions, respectively. We demonstrate that the canonical merging of models sharing a common subsystem corresponds to computing a pushout in the category of submodels, while merging models sharing a common abstraction corresponds to a pullback in the category of abstractions. We establish sufficient topological and domain-level conditions under which these universal constructions exist.} }
Endnote
%0 Conference Paper %T One Model to Rule Them All: Canonically Gluing Causal Models Along Shared Substructures %A Markus Englberger %A Devendra Singh Dhami %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-englberger26a %I PMLR %P 1474--1497 %U https://proceedings.mlr.press/v337/englberger26a.html %V 337 %X Causal {Bayesian} Networks (CBNs) provide a framework for reasoning about interventions, but analyzing complex systems often requires working with multiple overlapping models or hierarchical levels of granularity. We study how to canonically merge separate causal models that share a common substructure or abstract representation. We formalize this problem using category theory. We construct two distinct categories of causal models where morphisms are defined by maps that commute with interventions. Depending on whether these maps are injective or surjective, they represent causal submodels or causal abstractions, respectively. We demonstrate that the canonical merging of models sharing a common subsystem corresponds to computing a pushout in the category of submodels, while merging models sharing a common abstraction corresponds to a pullback in the category of abstractions. We establish sufficient topological and domain-level conditions under which these universal constructions exist.
APA
Englberger, M. & Dhami, D.S.. (2026). One Model to Rule Them All: Canonically Gluing Causal Models Along Shared Substructures. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:1474-1497 Available from https://proceedings.mlr.press/v337/englberger26a.html.

Related Material