Efficient Differentiable Discovery of Causal Order

ICLR 2026 Conference Submission17226 Authors

Keywords: causality, causal inference, causal discovery, causal structure learning, causal regularisation

Abstract: We introduce a differentiable and scalable regularizer for causal order, which can be integrated into gradient-based learning systems to inject causal inductive bias. Our approach builds on Intersort (Chevalley et al., 2025), a recently proposed score-based method that infers causal orderings from interventional data. While effective, Intersort requires discrete combinatorial optimization, making it computationally expensive and non-differentiable. We address this limitation by relaxing the score with continuous optimization techniques, including differentiable sorting and ranking, yielding a differentiable surrogate objective. The resulting formulation can be used as a regularizer to encode prior knowledge about causal order—whether derived from interventions, domain heuristics, or learned proxies. As a proof of concept, we instantiate this regularizer using single-variable interventions and demonstrate significant improvements in causal discovery tasks across diverse synthetic datasets. Our work enables scalable, differentiable, and flexible integration of causal order into modern learning systems.

Primary Area: causal reasoning

Submission Number: 17226