Analytic DAG Constraints for Differentiable DAG Learning

Recovering the underlying Directed Acyclic Graph (DAG) structures from observational data presents a formidable challenge, partly due to the combinatorial nature of the DAG-constrained optimization problem. Recently, researchers have identified gradient vanishing as one of the primary obstacles in differentiable DAG learning and have proposed several DAG constraints to mitigate this issue. By developing the necessary theory to establish a connection between analytic functions and DAG constraints, we demonstrate that analytic functions from the set $\{f(x) = c_0 + \sum_{i=1}^{\infty}c_ix^i | \forall i > 0, c_i > 0; r = \lim_{i\rightarrow \infty}c_{i}/c_{i+1} > 0\}$ can be employed to formulate effective DAG constraints. Furthermore, we establish that this set of functions is closed under several functional operators, including differentiation, summation, and multiplication. Consequently, these operators can be leveraged to create novel DAG constraints based on existing ones. Using these properties, we design a series of DAG constraints and develop an efficient algorithm to evaluate them. Experiments in various settings demonstrate that our DAG constraints outperform previous state-of-the-art comparators. Our implementation is available atthis https URL.

@article{zhang2025_2503.19218,
  title={ Analytic DAG Constraints for Differentiable DAG Learning },
  author={ Zhen Zhang and Ignavier Ng and Dong Gong and Yuhang Liu and Mingming Gong and Biwei Huang and Kun Zhang and Anton van den Hengel and Javen Qinfeng Shi },
  journal={arXiv preprint arXiv:2503.19218},
  year={ 2025 }
}