mlsanityData to 14 Oct 2026

Analytic DAG Constraints for Differentiable DAG Learning

arXiv 2503.19218 ↗First posted 24 Mar 2025cs.LG stat.MLcited by 5

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Abstract (arXiv)

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) = c0 + sumi=1∞cixi | forall i > 0, ci > 0; r = limirightarrow ∞ci/ci+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 at https://github.com/zzhang1987/AnalyticDAGLearning.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 15 of its 39 references that are in the map. First posted on arXiv 24 Mar 2025.

Builds on

15 of 39 references.

References · 15

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  3. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 331
  4. 2019Gradient-Based Neural DAG Learningcited by 227
  5. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 211
  6. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
  7. 2013Causal Inference in the Presence of Latent Variables and Selection Biascited by 166
  8. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 161
  9. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 140
  10. 2013High-dimensional learning of linear causal networks via inverse covariance estimationcited by 87
  11. 2020DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networkscited by 66
  12. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
3 more
  1. 2020On the Convergence of Continuous Constrained Optimization for Structure Learningcited by 38
  2. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 36
  3. 2022Truncated Matrix Power Iteration for Differentiable DAG Learningcited by 23

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2025Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Modelscited by 2
  2. 2025Differentiable Structure Learning and Causal Discovery for General Binary Datacited by 0
  3. 2026Efficient Differentiable Causal Discovery via Reliable Super-Structure Learningcited by 0
  4. 2026Structure Learning on Clustered Datacited by 0
  5. 2026Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificatescited by 0