Title: Efficient Differentiable Discovery of Causal Order
Primary area: causal reasoning
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.