# Efficient Differentiable Causal Discovery via Reliable Super-Structure Learning

arXiv: https://arxiv.org/abs/2601.05474 · HTML: https://mlsanity.com/paper/2601.05474/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 43 references that are in the map.
- First posted on arXiv 9 Jan 2026.

## Builds on (most cited first, 22 of 22)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [Truncated Matrix Power Iteration for Differentiable DAG Learning](https://mlsanity.com/paper/2208.14571/) (2022)
- [Iterative Causal Discovery in the Possible Presence of Latent Confounders and Selection Bias](https://mlsanity.com/paper/2111.04095/) (2021)
- [Differentiable Causal Discovery Under Latent Interventions](https://mlsanity.com/paper/2203.02336/) (2022)
- [Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions](https://mlsanity.com/paper/2201.05666/) (2022)
- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learning](https://mlsanity.com/paper/2303.12703/) (2023)
- [Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)](https://mlsanity.com/paper/2406.10537/) (2024)
- [Analytic DAG Constraints for Differentiable DAG Learning](https://mlsanity.com/paper/2503.19218/) (2025)
- [The Robustness of Differentiable Causal Discovery in Misspecified Scenarios](https://mlsanity.com/paper/2510.12503/) (2025)

## Abstract (arXiv)

Recently, differentiable causal discovery has emerged as a promising approach to improve the accuracy and efficiency of existing methods. However, when applied to high-dimensional data or data with latent confounders, these methods, often based on off-the-shelf continuous optimization algorithms, struggle with the vast search space, the complexity of the objective function, and the nontrivial nature of graph-theoretical constraints. As a result, there has been a surge of interest in leveraging super-structures to guide the optimization process. Nonetheless, learning an appropriate super-structure at the right level of granularity, and doing so efficiently across various settings, presents significant challenges. In this paper, we propose ALVGL, a novel and general enhancement to the differentiable causal discovery pipeline. ALVGL employs a sparse and low-rank decomposition to learn the precision matrix of the data. We design an ADMM procedure to optimize this decomposition, identifying components in the precision matrix that are most relevant to the underlying causal structure. These components are then combined to construct a super-structure that is provably a superset of the true causal graph. This super-structure is used to initialize a standard differentiable causal discovery method with a more focused search space, thereby improving both optimization efficiency and accuracy. We demonstrate the versatility of ALVGL by instantiating it across a range of structural causal models, including both Gaussian and non-Gaussian settings, with and without unmeasured confounders. Extensive experiments on synthetic and real-world datasets show that ALVGL not only achieves state-of-the-art accuracy but also significantly improves optimization efficiency, making it a reliable and effective solution for differentiable causal discovery.