Title: Unlocking Temporal Causal Structure Through Smooth Differentiable Optimization

Abstract: Identifying causal relationships involving instantaneous effects in multivariate time series presents significant challenges, primarily because the instantaneous structure is required to remain acyclic. Existing approaches typically address this by splitting the estimation of instantaneous and lagged effects into multi-stage workflows or by applying complex algebraic acyclicity constraints through augmented Lagrangian optimization; however, both strategies result in substantial computational overhead. To overcome these limitations, we introduce a novel methodology that employs the Gumbel--Sinkhorn operator to learn a differentiable permutation of variables. This process triangularizes the instantaneous coefficient matrix within a Structural Vector Autoregressive (SVAR) model according to the discovered order. By transforming acyclicity from a rigid constraint into a learnable parameterization, the structural validity is maintained throughout the optimization process. This approach facilitates unified, continuous optimization via gradient-based learning, thereby enhancing the efficiency of causal discovery in time series. Evaluated across three real-world benchmarks, our method outperforms 12 baseline models in both discovery accuracy and computational efficiency. Furthermore, on large-scale benchmarks, the proposed technique demonstrates robust scalability, delivering a speedup of over 6 times compared to competing methods.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC