Constructive Causal Abstraction and a Case Study in Mechanistic Interpretability

Existing frameworks in causal abstraction first propose a high-level causal model, and then verify whether its interventional effects agree with those of a given micro-level model - the two models are declared causally consistent when the discrepancy is zero. However, proposing a consistent macro causal model is difficult, because macro causal relations are almost never well-defined, since distinct micro-level interventions associated with the same apparent macro intervention can produce different effects. Our central insight is that causally consistent macro-level models can be obtained constructively: ill-defined macro interventions can be interpreted as missing variables on the macro level, and can be accounted for by introducing a complementary variable $q$ that retains omitted causally relevant state. In the linear case, $q$ has a unique form and we provide sufficient conditions for valid implementations to exist; in the nonlinear case, we provide an ODE-based algorithm for constructing implementations. We call this framework Constructive Causal Abstraction (CCA), and use CCA to formulate the difference between machine-learning model auditing and editing. With the Bias-in-Bios biographies dataset, we demonstrate that CCA allows practitioners to articulate assumptions when detecting the model's gender bias. Finally, CCA resolves a well-known paradox known as `interpretability illusion' which points to a mismatch between the subspace for editing and the one where the model implements a signal-to-output pathway.