Model Metamers Reveal Invariances in Graph Neural Networks

In recent years, deep neural networks have been extensively employed in perceptual systems to learn representations endowed with invariances, aiming to emulate the invariance mechanisms observed in the human brain. However, studies in the visual and auditory domains have confirmed that significant gaps remain between the invariance properties of artificial neural networks and those of humans. To investigate the invariance behavior within graph neural networks (GNNs), we introduce a model ``metamers'' generation technique. By optimizing input graphs such that their internal node activations match those of a reference graph, we obtain graphs that are equivalent in the model's representation space, yet differ significantly in both structure and node features. Our theoretical analysis focuses on two aspects: the local metamer dimension for a single node and the activation-induced volume change of the metamer manifold. Utilizing this approach, we uncover extreme levels of representational invariance across several classic GNN architectures. Although targeted modifications to model architecture and training strategies can partially mitigate this excessive invariance, they fail to fundamentally bridge the gap to human-like invariance. Finally, we quantify the deviation between metamer graphs and their original counterparts, revealing unique failure modes of current GNNs and providing a complementary benchmark for model evaluation.