Differentiable Causal Search

Kaveh Aryan, Hana Chockler, Mohammad Reza Mousavi
Proceedings of the Fifth Conference on Causal Learning and Reasoning, PMLR 323:1693-1708, 2026.

Abstract

Actual causality–identifying the causes of particular events–is formalised by the Halpern–Pearl (HP) definitions via counterfactual reasoning over structural causal models. Computing HP causes requires solving a combinatorial optimisation problem that is, depending on the variant, \(D^P_1\)-complete or worse. We propose a differentiable approximation of HP causality that leverages the robustness semantics of logical specifications and additive intervention relaxations. Specifically, we replace discrete satisfiability constraints with continuous robustness scores, and model interventions as soft variable shifts rather than hard graph surgeries. This, along with a sparsity relaxation, allows for using continuous optimisation techniques such as gradient descent. Experiments on synthetic graphs show that our method, on average, approximates the true causes with a $\pm$5 % error margin, while achieving at least a 60$\times$ speedup. The framework also supports fine-grained control over additional causal properties such as the desired counterfactual robustness.

Cite this Paper

BibTeX
@InProceedings{pmlr-v323-aryan26a, title = {Differentiable Causal Search}, author = {Aryan, Kaveh and Chockler, Hana and Mousavi, Mohammad Reza}, booktitle = {Proceedings of the Fifth Conference on Causal Learning and Reasoning}, pages = {1693--1708}, year = {2026}, editor = {Mazaheri, Bijan and Hanson, Niels Richard}, volume = {323}, series = {Proceedings of Machine Learning Research}, month = {06--08 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v323/main/assets/aryan26a/aryan26a.pdf}, url = {https://proceedings.mlr.press/v323/aryan26a.html}, abstract = {Actual causality–identifying the causes of particular events–is formalised by the Halpern–Pearl (HP) definitions via counterfactual reasoning over structural causal models. Computing HP causes requires solving a combinatorial optimisation problem that is, depending on the variant, \(D^P_1\)-complete or worse. We propose a differentiable approximation of HP causality that leverages the robustness semantics of logical specifications and additive intervention relaxations. Specifically, we replace discrete satisfiability constraints with continuous robustness scores, and model interventions as soft variable shifts rather than hard graph surgeries. This, along with a sparsity relaxation, allows for using continuous optimisation techniques such as gradient descent. Experiments on synthetic graphs show that our method, on average, approximates the true causes with a $\pm$5 % error margin, while achieving at least a 60$\times$ speedup. The framework also supports fine-grained control over additional causal properties such as the desired counterfactual robustness.} }
Endnote
%0 Conference Paper %T Differentiable Causal Search %A Kaveh Aryan %A Hana Chockler %A Mohammad Reza Mousavi %B Proceedings of the Fifth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2026 %E Bijan Mazaheri %E Niels Richard Hanson %F pmlr-v323-aryan26a %I PMLR %P 1693--1708 %U https://proceedings.mlr.press/v323/aryan26a.html %V 323 %X Actual causality–identifying the causes of particular events–is formalised by the Halpern–Pearl (HP) definitions via counterfactual reasoning over structural causal models. Computing HP causes requires solving a combinatorial optimisation problem that is, depending on the variant, \(D^P_1\)-complete or worse. We propose a differentiable approximation of HP causality that leverages the robustness semantics of logical specifications and additive intervention relaxations. Specifically, we replace discrete satisfiability constraints with continuous robustness scores, and model interventions as soft variable shifts rather than hard graph surgeries. This, along with a sparsity relaxation, allows for using continuous optimisation techniques such as gradient descent. Experiments on synthetic graphs show that our method, on average, approximates the true causes with a $\pm$5 % error margin, while achieving at least a 60$\times$ speedup. The framework also supports fine-grained control over additional causal properties such as the desired counterfactual robustness.
APA
Aryan, K., Chockler, H. & Mousavi, M.R.. (2026). Differentiable Causal Search. Proceedings of the Fifth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 323:1693-1708 Available from https://proceedings.mlr.press/v323/aryan26a.html.

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