发表机构
PES University（PES大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究揭示了增广拉格朗日因果发现中「引导而非约束」设计的两个失效原因，通过理论分析和3072次训练实验验证，提出DADU松弛规则违反必要条件，且相关性匹配目标存在边方向绑定问题。
AI 中文摘要
可微分因果发现方法越来越多地将专家先验编码为增广拉格朗日（ALM）惩罚所强制的禁边约束，其假设是数据自适应松弛机制会弱化并最终覆盖与数据持续矛盾的规则。我们展示了这种被称为「引导而非约束」的设计因两个独立且精确表征的原因失效，且直接修复这两个原因仅能部分恢复性能。首先，序贯惩罚递增的ALM会在任何反事实检查能检测到之前就抑制被错误禁止的真实边：我们给出任何自适应松弛必须满足的三个必要条件以避免此问题（命题1），证明本文作为研究对象引入的自然松弛规则DADU违反所有三个条件（推论1），并在3072次训练运行中确认该失效，这些运行涵盖节点数从4到32的图，在DADU下，单个错误先验会在87%-97%的试验中抑制一条真实边。其次，独立于对该机制的任何修复，我们以闭式形式证明，标准相关性匹配目标将一条真实边与其反向边绑定到完全相同的成本，恰好为2r²（引理1），这并非因为基础等方差模型不可识别，而是因为归一化为相关性会丢弃使其可识别所需的方差信息；相反，协方差匹配以至少w₀⁴的可证明余量分离两个方向（引理2）。
英文摘要
Differentiable causal discovery methods increasingly encode expert priors as forbidden-edge constraints enforced by an Augmented Lagrangian (ALM) penalty, on the assumption that a data-adaptive relaxation mechanism will discount and eventually override a rule the data consistently contradicts. We show this design, which we call \emph{guide, not bind}, fails for two independent, precisely characterized reasons, and that directly repairing both restores it only partially. First, sequential penalty-ramping ALM suppresses a wrongly-forbidden true edge before any counterfactual check can detect it: we give three necessary conditions any adaptive relaxation must satisfy to avoid this (Proposition~\ref{prop:conditions}), prove that DADU---the natural relaxation rule this paper introduces as the object of study---violates all three (Corollary~\ref{cor:dadu_failure}), and confirm the failure across 3{,}072 training runs spanning graphs from 4 to 32 nodes, where a single wrong prior suppresses a true edge in 87--97\% of trials under DADU. Second, and independent of any fix to the mechanism, we prove in closed form that the standard correlation-matching objective ties a true edge and its reverse to an identical cost of exactly $2r^2$ (Lemma~\ref{lem:tie}), not because the underlying equal-variance model is unidentifiable, but because normalizing to correlation discards exactly the variance information that would make it identifiable; covariance matching instead separates the two directions by a provable margin of at least $w_0^4$ (Lemma~\ref{lem:separation}).
Comments29 pages, 6 figures
