A real SchNet-family GNN's 128-parameter QM9 molecular embedding space reduces to around 5 effective parameters, with sharp linear boundaries separating chemical moieties

Dimension reduction and linear discriminant analysis applied to the hidden-layer embedding vectors of a real SchNet-family GNN trained on the real QM9 molecular dataset show the fully-trained 128-parameter embedding space reduces to a low parametric space of around 5 important parameters [el-samman-etal-2024-global-geometry-chemical-gnn-moieties] Sharp linear boundaries separate chemical moieties within this reduced embedding space, with classification error below 5x10^-4 [el-samman-etal-2024-global-geometry-chemical-gnn-moieties] Euclidean distance in the embedding space functions as a molecular similarity measure competitive with the hand-engineered SOAP descriptor, and embedding coordinates linearly predict pKa and NMR chemical-shift observables [el-samman-etal-2024-global-geometry-chemical-gnn-moieties]