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<p>Modern image-analysis pipelines often convert images into structured semantic variables, such as facial attributes, object concepts, and scene descriptors. Learning directed dependencies among these variables can produce interpretable visual semantic graphs, but continuous directed acyclic graph learning is limited by the cost of enforcing acyclicity. We present polyDAG, a polynomial acyclicity framework for efficient continuous causal discovery in visual semantic graphs. polyDAG replaces the matrix-exponential acyclicity constraint with a finite-polynomial trace constraint and proves that the new constraint is zero exactly for acyclic graphs. We further derive a geometric-series implementation that avoids the explicit summation loop while preserving the same acyclicity condition. Experiments on synthetic Erdős–Rényi graphs and CelebA facial visual attributes show that polyDAG improves efficiency and structure recovery. Averaged over the revised synthetic protocol (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(d \in \{100,200,500\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>∈</mo> <mo stretchy="false">{</mo> <mn>100</mn> <mo>,</mo> <mn>200</mn> <mo>,</mo> <mn>500</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>), polyDAG reduces mean structural Hamming distance from 318.4 to 285.4 and improves mean F1 score from 0.725 to 0.756. At 100 nodes, the geometric variant runs in 3.44&#xa0;s compared with 5.16&#xa0;s for the exponential baseline, a 33.4% speedup. Code and data are publicly available at <a href="https://github.com/wenhaoz-fengcai/polyDAG">https://github.com/wenhaoz-fengcai/polyDAG</a>.</p>

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polyDAG: polynomial acyclicity constraints for efficient continuous causal discovery in visual semantic graphs

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • Wenhao Zhang,
  • Ramin Ramezani,
  • Tao Han,
  • Kai Hwang,
  • Minyi Guo

摘要

Modern image-analysis pipelines often convert images into structured semantic variables, such as facial attributes, object concepts, and scene descriptors. Learning directed dependencies among these variables can produce interpretable visual semantic graphs, but continuous directed acyclic graph learning is limited by the cost of enforcing acyclicity. We present polyDAG, a polynomial acyclicity framework for efficient continuous causal discovery in visual semantic graphs. polyDAG replaces the matrix-exponential acyclicity constraint with a finite-polynomial trace constraint and proves that the new constraint is zero exactly for acyclic graphs. We further derive a geometric-series implementation that avoids the explicit summation loop while preserving the same acyclicity condition. Experiments on synthetic Erdős–Rényi graphs and CelebA facial visual attributes show that polyDAG improves efficiency and structure recovery. Averaged over the revised synthetic protocol ( \(d \in \{100,200,500\}\) d ∈ { 100 , 200 , 500 } ), polyDAG reduces mean structural Hamming distance from 318.4 to 285.4 and improves mean F1 score from 0.725 to 0.756. At 100 nodes, the geometric variant runs in 3.44 s compared with 5.16 s for the exponential baseline, a 33.4% speedup. Code and data are publicly available at https://github.com/wenhaoz-fengcai/polyDAG.