Bridging Distance and Spectral Positional Encodings via Anchor-Based Diffusion Geometry Approximation

ACL ARR 2026 January Submission4242 Authors

Keywords: Positional encoding; Diffusion geometry; Distance encoding; Laplacian eigenmaps; Drug-drug interaction prediction

Abstract: 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 Nystr\"om scheme closely recovers diffusion geometry, and both Laplacian and distance encodings substantially outperform a no-encoding baseline.

Paper Type: Long

Research Area: Mathematical, Symbolic, Neurosymbolic, and Logical Reasoning

Research Area Keywords: Machine Learning for NLP, Interpretability and Analysis of Models for NLP

Contribution Types: Model analysis & interpretability, Approaches to low-resource settings

Languages Studied: Not applicable

Submission Number: 4242