Differentiable Causal Search

Kaveh Aryan, Hana Chockler, Mohammad Reza Mousavi

Keywords: actual causality, halpern-pearl definition, gradient-based optimisation

TL;DR: We introduce a differentiable approximation of Halpern–Pearl causality that replaces discrete interventions with continuous optimisations, achieving near-accurate causes with large speedups.

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 ±5 \% error margin, while achieving at least a 60× speedup. The framework also supports fine-grained control over additional causal properties such as the desired counterfactual robustness.

Submission Number: 104