Extending a manifold triangulation benchmark reveals GNNs and HOMP can saturate it with proper representations, yet existing models fail to generalize beyond combinatorial structure.
Diversity curves track structural spread across graph coarsening levels to yield interpretable, size-invariant graph embeddings for clustering, visualization, and comparison.
Topological and geometric embedding measures are redundant, so Unified Topological Signatures holistically characterize spaces to predict model properties and retrieval performance.