# Guide, Not Bind: Why Defeasible Priors Fail in Augmented Lagrangian Causal Discovery

arXiv: https://arxiv.org/abs/2609.03442 · HTML: https://mlsanity.com/paper/2609.03442/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Builds on (most cited first, 17 of 17)

- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
- [Two-Player Games for Efficient Non-Convex Constrained Optimization](https://mlsanity.com/paper/1804.06500/) (2018)
- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [Probably Approximately Correct Constrained Learning](https://mlsanity.com/paper/2006.05487/) (2020)
- [The impact of prior knowledge on causal structure learning](https://mlsanity.com/paper/2102.00473/) (2021)
- [Stable Differentiable Causal Discovery](https://mlsanity.com/paper/2311.10263/) (2023)
- [Large Language Models are Effective Priors for Causal Graph Discovery](https://mlsanity.com/paper/2405.13551/) (2024)
- [Dagma-DCE: Interpretable, Non-Parametric Differentiable Causal Discovery](https://mlsanity.com/paper/2401.02930/) (2024)
- [The Robustness of Differentiable Causal Discovery in Misspecified Scenarios](https://mlsanity.com/paper/2510.12503/) (2025)

## Abstract (arXiv)

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 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~refprop:conditions), prove that DADU---the natural relaxation rule this paper introduces as the object of study---violates all three (Corollary~refcor:dadufailure), 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 2r2 (Lemma~reflem: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 w04 (Lemma~reflem:separation).