Time-Series Causal Discovery via Differentiable Permutations

ICLR 2026 Conference Submission14458 Authors

Keywords: Causal discovery, Time series, Acyclicity

Abstract: Causal discovery with instantaneous effects in multivariate time series is challenging, as the instantaneous structure must be acyclic. Prior methods enforce this by either recovering a causal order through discrete combinatorial search or imposing algebraic acyclicity constraints via complex augmented Lagrangian optimization, both of which incur high computational cost. In this work, we propose a fundamentally different method: we learn a differentiable permutation of variables using the Gumbel–Sinkhorn operator and triangularize the instantaneous coefficient matrix of a Structural Vector Autoregressive (SVAR) model in learned order. This converts acyclicity from a hard constraint into a parameterization and keeps it valid throughout optimization. In doing so, our method enables unified, continuous optimization with gradient-based learning, leading to improved efficiency in time series causal discovery. Across three real-world benchmarks, our method achieves the best overall performance compared with 12 baselines in both discovery accuracy and efficiency. On the large-scale benchmark, it further demonstrates strong scalability, achieving more than a 6× speedup over competing methods.

Primary Area: causal reasoning

Submission Number: 14458