Analytic DAG Constraints for Differentiable DAG Learning
Zhang, Zhen Ng, Ignavier Gong, Dong Liu, Yuhang Gong, Mingming Huang, Biwei Zhang, Kun Hengel, Anton Shi, Javen Qinfeng
Zhang, Zhen
Ng, Ignavier
Gong, Dong
Liu, Yuhang
Gong, Mingming
Huang, Biwei
Zhang, Kun
Hengel, Anton
Shi, Javen Qinfeng
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Department
Machine Learning
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Conference proceeding
Date
2025
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Language
English
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Abstract
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 (Equation presented) 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 at https://github.com/zzhang1987/AnalyticDAGLearning. © 2025 13th International Conference on Learning Representations, ICLR 2025. All rights reserved.
Citation
Z. Zhang et al., “Analytic DAG Constraints for Differentiable DAG Learning,” International Conference on Representation Learning, vol. 2025, pp. 15862–15887, May 2025, Accessed: Jul. 22, 2025
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13th International Conference on Learning Representations, ICLR 2025
Conference
13th International Conference on Learning Representations, ICLR 2025
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Source
13th International Conference on Learning Representations, ICLR 2025
Publisher
International Conference on Learning Representations, ICLR