Causal Graphs, Markov Properties and Do-calculus for Stochastic Differential Equations

What the math gives to ML

The paper provides a path-space causal semantics for stochastic differential systems, including adapted coefficients, interventions, cyclic additive-noise models, and temporal splitting. The transferable asset is a principled way to impose causal structure on continuous-time latent dynamics while preserving well-posedness under interventions and long rollouts. A practical neural implementation is a graph-masked neural SDE whose coordinate-wise drift and diffusion functions read only parent trajectories, combined with an empirical Lipschitz penalty derived from the paper's existence conditions.