# Aitchison Embeddings for Learning Compositional Graph Representations

arXiv: https://arxiv.org/abs/2605.00716 · HTML: https://mlsanity.com/paper/2605.00716/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [XGNN: Towards Model-Level Explanations of Graph Neural Networks](https://mlsanity.com/paper/2006.02587/) (2020)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Explainability Techniques for Graph Convolutional Networks](https://mlsanity.com/paper/1905.13686/) (2019)
- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models](https://mlsanity.com/paper/2005.07959/) (2020)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [ProtGNN: Towards Self-Explaining Graph Neural Networks](https://mlsanity.com/paper/2112.00911/) (2021)
- [vGraph: A Generative Model for Joint Community Detection and Node Representation Learning](https://mlsanity.com/paper/1906.07159/) (2019)
- [Is a Single Embedding Enough? Learning Node Representations that Capture Multiple Social Contexts](https://mlsanity.com/paper/1905.02138/) (2019)
- [Network Representation Learning: From Preprocessing, Feature Extraction to Node Embedding](https://mlsanity.com/paper/2110.07582/) (2021)
- [Learning Role-based Graph Embeddings](https://mlsanity.com/paper/1802.02896/) (2018)
- [Graph Neural Networks Including Sparse Interpretability](https://mlsanity.com/paper/2007.00119/) (2020)
- [A Hierarchical Block Distance Model for Ultra Low-Dimensional Graph Representations](https://mlsanity.com/paper/2204.05885/) (2022)
- [Characterizing Polarization in Social Networks using the Signed Relational Latent Distance Model](https://mlsanity.com/paper/2301.09507/) (2023)
- [HM-LDM: A Hybrid-Membership Latent Distance Model](https://mlsanity.com/paper/2206.03463/) (2022)
- [What Do GNNs Actually Learn? Towards Understanding their Representations](https://mlsanity.com/paper/2304.10851/) (2023)
- [Signed Graph Autoencoder for Explainable and Polarization-Aware Network Embeddings](https://mlsanity.com/paper/2409.10452/) (2024)
- [The Signed Two-Space Proximity Model for Learning Representations in Protein-Protein Interaction Networks](https://mlsanity.com/paper/2503.03904/) (2025)

## Built on by (most cited first, 2 of 2)

- [Rank Is Not Capacity: Spectral Occupancy for Latent Graph Models](https://mlsanity.com/paper/2605.11142/) (2026)
- [Which Question Is Your Attention Metric Answering? Attention Rows as Compositional Data](https://mlsanity.com/paper/2608.14712/) (2026)

## Abstract (arXiv)

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.