New Causal Discovery Algorithms Uncover Latent Confounders Using Lie Bracket Geometry

Recent theoretical work, Kan-Do-Calculus (KDC), has established a categorical framework for causal inference, distinguishing between passive observation and active intervention. Building on this, new research introduces two causal discovery algorithms designed to identify latent confounding structures in smooth statistical settings. These algorithms leverage the information-geometric and categorical implications of KDC. The core idea involves using Radon-Nikodym derivatives between observational and interventional measures to induce local causal vector fields. Failures of these fields to close under Lie brackets are interpreted as "Frobenius residuals," signaling unmodeled or latent structures. The first algorithm, BRIDGE (Bracket Residuals for Interventional Discovery and Geometric Estimation), combines an interventional density engine with a geometric screen. This screen proposes a high-recall family of admissible causal arrows, identifies non-closing pairs as potential latent obstructions, and then passes a reduced family to downstream discovery routines. The second algorithm, Spectral Kan-Do Flow Matching (SKFM), learns amortized intervention fields and spectrally factors latent curvature, directly exposing the geometric endpoint that BRIDGE points towards. Extensive experiments demonstrate that both BRIDGE and SKFM can effectively discover causal models even when latent confounders are present, dramatically reducing the super-exponential search space of possible Directed Acyclic Graphs (DAGs). This work introduces a new paradigm for causal discovery, inferring latent structure directly from the geometry of intervention-induced flows.