Aitchison Embeddings for Learning Compositional Graph Representations

2026-05-01

AI Summary

This work addresses the limited interpretability of existing graph embedding methods, which often fail to elucidate the relationship between learned features and underlying graph structure. The authors propose a composable graph embedding framework grounded in Aitchison geometry, representing nodes as compositional data on the simplex and mapping them into Euclidean space via isometric log-ratio (ILR) coordinates. This approach preserves the relative relationships among components while enabling unconstrained optimization. The resulting embeddings are inherently interpretable and exhibit subcompositional coherence, allowing for ablation-style analysis of how individual compositional factors influence node representations and downstream predictions. Experimental results demonstrate that the method achieves performance on par with strong baselines in node classification and link prediction tasks, while offering native interpretability without requiring post-hoc explanation techniques.

Abstract

Representation learning is central to graph machine learning, powering tasks such as link prediction and node classification. However, most graph embeddings are hard to interpret, offering limited insight into how learned features relate to graph structure. Many networks naturally admit a role-mixture view, where nodes are best described as mixtures over latent archetypal factors. Motivated by this structure, we propose a compositional graph embedding framework grounded in Aitchison geometry, the canonical geometry for comparing mixtures. Nodes are represented as simplex-valued compositions and embedded via isometric log-ratio (ILR) coordinates, which preserve Aitchison distances while enabling unconstrained optimization in Euclidean space. This yields intrinsically interpretable embeddings whose geometry reflects relative trade-offs among archetypes and supports coherent behavior under component restriction; we consider both fixed and learnable ILR bases. Across node classification and link prediction, our method achieves competitive performance with strong baselines while providing explainability by construction rather than post-hoc. Finally, subcompositional coherence enables principled component restriction: removing and renormalizing subsets preserves a well-defined geometry, which we exploit via subcompositional dimensionality removal to probe how archetype groups influence representations and predictions.

Problem

• graph embeddings
• interpretability
• compositional data
• Aitchison geometry
• role-mixture

Innovation

• Aitchison geometry
• compositional embeddings
• isometric log-ratio (ILR)
• subcompositional coherence
• interpretable graph representation