Feature interaction graphs for exact interpretable learning solver selection: an empirical diagnostic study

Exact interpretable learning is attractive in regulated decision settings, but solver runtime can vary substantially across datasets and solver families. We introduce structural meta-features derived from Feature Interaction Graphs (FIG s) as interpretable signals for solver selection. We construct FIG s from binarized tabular data using pairwise mutual information and extract topology-aware signatures such as density and estimated treewidth. Using a transparent shallow decision-tree selector, we demonstrate that FIG features establish an interpretable structural view of solver behavior, complementing basic, statistical, and landmarking meta-features. Experiments on OpenML classification tasks show that topology-aware profiling exposes meaningful structural variation across datasets, although benchmark saturation prevents clear end-to-end routing gains over strong simple baselines. Our results validate FIG as a principled, interpretable diagnostic tool for algorithm selection in exact learning; its diagnostic relevance becomes apparent on harder instances where solver runtime separation is substantial.