I’m an AI Researcher at Truth Audit Labs working on AI safety products. I have a background in formal methods and causal inference. Previously, I wrote software for Google Distributed Cloud.
A dependency-level account of why graph surgery and constant mechanism replacement describe the same intervention, together with laws for exactness, sequential interventions, and ancestor-local outcomes. The principal results are mechanized in Lean 4.
The do-operator is described graphically by deleting arrows into its targets and functionally by replacing their mechanisms with constants. To call these operations equivalent is not yet a mathematical statement: one returns a graph and remembers only the targets, whereas the other returns mechanisms and also remembers the imposed values. We make a dependency-level comparison precise for deterministic acyclic structural causal models with finitely many endogenous variables. If Graph(F) extracts the dependencies of a mechanism family F, our main theorem shows that replacing target mechanisms removes exactly the dependencies removed by graph surgery. For a model whose graph may contain unused arrows, we characterize when the same equality holds with the supplied graph; we then define the intervened model, characterize its run, show how sequential interventions combine, and prove that an outcome depends only on interventions at its actual dependency ancestors.
@misc{makhija2026graphsurgery,title={Graph Surgery and the Do-Operator: A Precise Correspondence for Acyclic Structural Causal Models},author={Makhija, Satpreet},year={2026},month=aug,note={Preprint},eprint={2608.17634},archiveprefix={arXiv},primaryclass={cs.AI},}
