# Differentiable Constraint-Based Causal Discovery

arXiv: https://arxiv.org/abs/2510.22031 · HTML: https://mlsanity.com/paper/2510.22031/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 58 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 25 of 25)

- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [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)
- [Gradient Vaccine: Investigating and Improving Multi-task Optimization in Massively Multilingual Models](https://mlsanity.com/paper/2010.05874/) (2020)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [A Langevin-like Sampler for Discrete Distributions](https://mlsanity.com/paper/2206.09914/) (2022)
- [Learning to Solve Combinatorial Optimization Problems on Real-World Graphs in Linear Time](https://mlsanity.com/paper/2006.03750/) (2020)
- [NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge](https://mlsanity.com/paper/2109.04286/) (2021)
- [BayesDAG: Gradient-Based Posterior Inference for Causal Discovery](https://mlsanity.com/paper/2307.13917/) (2023)
- [Probabilistic Evaluation of Sequential Plans from Causal Models with Hidden Variables](https://mlsanity.com/paper/1302.4977/) (2013)
- [Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)](https://mlsanity.com/paper/1301.7412/) (2013)
- [Characterization and Learning of Causal Graphs with Small Conditioning Sets](https://mlsanity.com/paper/2301.09028/) (2023)
- [Recovering Causal Structures from Low-Order Conditional Independencies](https://mlsanity.com/paper/2010.02675/) (2020)
- [logLTN: Differentiable Fuzzy Logic in the Logarithm Space](https://mlsanity.com/paper/2306.14546/) (2023)

## Built on by (most cited first, 4 of 4)

- [Enes Causal Discovery](https://mlsanity.com/paper/2603.24436/) (2026)
- [PRCD-MAP: Learning How Much to Trust Imperfect Priors in Causal Discovery](https://mlsanity.com/paper/2605.01669/) (2026)
- [EML-CD: Causal Mechanism Recovery via EML Symbolic Trees in Structure Learning](https://mlsanity.com/paper/2606.05942/) (2026)
- [SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discovery](https://mlsanity.com/paper/2608.04930/) (2026)

## Abstract (arXiv)

Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly categorized as constraint-based or score-based approaches. Constraint-based methods offer rigorous causal discovery but are often hindered by small sample sizes, while score-based methods provide flexible optimization but typically forgo explicit conditional independence testing. This work explores a third avenue: developing differentiable d-separation scores, obtained through a percolation theory using soft logic. This enables the implementation of a new type of causal discovery method: gradient-based optimization of conditional independence constraints. Empirical evaluations demonstrate the robust performance of our approach in low-sample regimes, surpassing traditional constraint-based and score-based baselines on a real-world dataset. Code and data of the proposed method are publicly available at https://github.com/PurdueMINDS/DAGPA.