# Latent Confounded Causal Discovery via Lie Bracket Geometry

arXiv: https://arxiv.org/abs/2606.19610 · HTML: https://mlsanity.com/paper/2606.19610/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 68 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 20 of 20)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [ParceLiNGAM: A causal ordering method robust against latent confounders](https://mlsanity.com/paper/1303.7410/) (2013)
- [Causal Discovery with Latent Confounders Based on Higher-Order Cumulants](https://mlsanity.com/paper/2305.19582/) (2023)
- [Large Causal Models from Large Language Models](https://mlsanity.com/paper/2512.07796/) (2025)
- [Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants](https://mlsanity.com/paper/2506.05202/) (2025)
- [PROMETHEUS: Automating Deep Causal Research Integrating Text, Data and Models](https://mlsanity.com/paper/2605.12835/) (2026)
- [Decentralized Causal Discovery using Judo Calculus](https://mlsanity.com/paper/2510.23942/) (2025)
- [Causal Density Functions](https://mlsanity.com/paper/2606.00754/) (2026)
- [Differentiable Causal Discovery of Linear Non-Gaussian Acyclic Models Under Unmeasured Confounding](https://mlsanity.com/paper/2501.12854/) (2025)

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

- [Infinitesimal Causality](https://mlsanity.com/paper/2606.24621/) (2026)
- [Odyssey: Constructing Verifiable Local Truth-Preserving Foundation Models](https://mlsanity.com/paper/2606.27593/) (2026)
- [Agentic Skill Optimization over Lie Algebroids](https://mlsanity.com/paper/2607.11493/) (2026)
- [Learning in Infinitesimal Non-Compositional Sketches](https://mlsanity.com/paper/2607.15107/) (2026)

## Abstract (arXiv)

We study causal discovery from observational and interventional regimes when latent variables may affect the measured system. Our first algorithm, BRIDGE (Bracket Residuals for Interventional Discovery and Geometric Estimation), combines a density-ratio or transport engine with a high-recall geometric screen and passes the retained arrows to a score-based or differentiable discovery method. The main formulation and experiments use known single-node intervention targets; in that regime the screen is designed to retain candidate directed effects, while a downstream learner determines the final graph or equivalence-class representation. Our second algorithm, Spectral Kernel Flow Matching (SKFM), amortizes the response fields, summarizes residual nonclosure by a spectral visible-footprint subspace, and applies an order-dependent graph extractor. Direct extraction succeeds on calibrated chains and selected motifs, but is unstable on harder random DAGs when the order must be learned. On ten-node nonlinear random DAGs, the more reliable hybrid role of the geometry is as a candidate generator: calibrated SKFM/Bridge fields followed by local BIC scoring achieve mean directed F1simeq0.86. Sachs protein signaling provides a real-data stress test and supports a diagnostic, not fully identified, interpretation. The contribution is therefore a practical interventional screening pipeline, explicit guarantees for screen retention and residual-footprint rank under stated assumptions, and a falsifiable account of the boundary between geometric diagnostics and causal identification.