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Life sciences · Preprint
arXiv · September 3, 2026
Raises a question worth testing. It does not answer one.
This preprint demonstrates through theoretical proofs and computational validation that a widely-used approach to encoding expert knowledge in causal discovery algorithms (Augmented Lagrangian penalty with adaptive relaxation) fails in two mathematically distinct ways: sequential penalty ramping suppresses true edges before detection, and correlation-matching objectives create unresolvable symmetries. The authors propose covariance matching as a partial remedy.
Theoretical analysis with computational validation.
A single wrong prior suppresses a true edge in 87–97% of trials under DADU across 3,072 training runs on graphs with 4 to 32 nodes Sequential penalty-ramping Augmented Lagrangian method suppresses wrongly-forbidden true edges before counterfactual verification can detect them Correlation-matching objective ties a true edge and its reverse to identical cost of exactly 2r²
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This is a theoretical analysis identifying failure modes in causal discovery algorithms; it raises mechanistic concerns rather than answering an empirical clinical or applied question.
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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}).
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