Bridging Distance and Spectral Positional Encodings via Anchor-Based Diffusion Geometry Approximation
This work addresses a gap in molecular graph learning by clarifying the connection between encoding methods, though it appears incremental as it builds on existing techniques without introducing a new paradigm.
The paper tackled the problem of understanding the relationship between spectral and distance positional encodings in molecular graph learning by interpreting distance encodings as a low-rank surrogate of diffusion geometry, with results showing that both encodings substantially outperform a no-encoding baseline on DrugBank molecular graphs.
Molecular graph learning benefits from positional signals that capture both local neighborhoods and global topology. Two widely used families are spectral encodings derived from Laplacian or diffusion operators and anchor-based distance encodings built from shortest-path information, yet their precise relationship is poorly understood. We interpret distance encodings as a low-rank surrogate of diffusion geometry and derive an explicit trilateration map that reconstructs truncated diffusion coordinates from transformed anchor distances and anchor spectral positions, with pointwise and Frobenius-gap guarantees on random regular graphs. On DrugBank molecular graphs using a shared GNP-based DDI prediction backbone, a distance-driven Nyström scheme closely recovers diffusion geometry, and both Laplacian and distance encodings substantially outperform a no-encoding baseline.