Decomposing Effects in Neural Causal Models

Structural causal models (SCMs) provide a principled foundation for causal reasoning, and neural causal models (NCMs) extend this framework by parameterizing causal mechanisms with neural networks. The classical formulation of NCMs assumes a specific architectural choice: a single function approximator per structural equation. In this work, we revisit this assumption and show that it represents only one point in a broader family of valid neural causal model parameterizations. Using interventions as an analytical lens and graph-based neural architectures as a concrete construction, we characterize how different parameter-sharing schemes over sub-mechanisms induce distinct members of the NCM family while preserving the same causal graph. This perspective yields two additional regimes beyond the classical formulation, which differ in how causal mechanisms are decomposed and parameterized within a unified structural framework. Together, these regimes demonstrate that architectural choices shape the causal semantics and expressivity of neural causal models, even when graphical structure is fixed. Relaxing structural assumptions further, we identify a class of partially causal models (PCMs) that support limited interventional or counterfactual queries without satisfying full SCM requirements, offering alternative trade-offs between causal fidelity and tractability. We place NCMs and PCMs within a unified expressivity spectrum between purely associational models and fully causal generative models, and illustrate these distinctions empirically using a graph-based variational autoencoder with interventional structure.