Hierarchical Attribution Networks: Composing Attribution‐Magnitude Flows Across Predictive Modules

Complex prediction systems often contain multiple fitted modules arranged as a directed acyclic graph (DAG), yet standard feature attribution typically explains one module at a time. We present Hierarchical Attribution Networks (HAN), a post hoc composition rule for tracing non‐negative attribution magnitude through a predictive DAG. For each observation and module, signed local feature attributions are retained, while their absolute magnitudes are normalized into routing coefficients. Terminal magnitude is the absolute deviation of the final model output from its explainer baseline. Flow is propagated upstream, stops at unresolved nodes whose attribution denominator is numerically negligible, and is aggregated over complete paths. This construction conserves routed magnitude by definition; it is not a new Shapley value, a causal decomposition or a claim of global efficiency. We evaluate the rule in a five‐module cascade using 2408 adults from the 2017–2018 National Health and Nutrition Examination Survey. Repeated nested out‐of‐fold prediction yielded weak but permutation‐detectable intermediate models (mean , , and ) and a final diabetes classifier with mean area under the receiver operating characteristic curve of 0.744. The direct age‐to‐risk path was dominant for 91.0% of participants. Synthetic experiments exposed signed‐ratio instability under cancellation and quantified sensitivity to collinearity and graph misspecification. Participant‐level bootstrap refitting, a KernelSHAP comparison and heterogeneous‐model analysis assessed stability and technical portability. HAN provides an auditable descriptive view of how local attribution magnitude is routed across modular predictors, conditional on the supplied graph, models and explainers.