Previous work has shown that node embedding methods can produce different representations and downstream predictions across repeated training runs, even when trained on the same data with identical hyperparameters. However, the role of embedding dimensionality in this instability remains poorly understood. In this work, we systematically analyze how embedding dimensionality affects the stability of embeddings from five widely used node embedding methods: ASNE, DGI, GraphSAGE, node2vec, and VERSE. We evaluate stability from both representational and functional perspectives across a broad range of dimensions, datasets, and repeated training runs, and relate the resulting stability patterns to predictive performance. Our results show that dimensionality can substantially affect embedding stability, although the observed effects depend strongly on the embedding method and stability notion considered. While node2vec and ASNE generally became more stable at higher dimensions, GraphSAGE and VERSE often exhibited non-monotonic behavior or decreasing stability. We further find that dimensions associated with high stability do not necessarily coincide with those yielding the strongest downstream performance. Overall, our findings demonstrate that embedding dimensionality can have a substantial impact on the stability of node embeddings and downstream predictions.
Embedding models (KGEMs) constitute the main link prediction approach to complete knowledge graphs. Standard evaluation protocols emphasize rank-based metrics such as MRR or Hits@K, but usually overlook the influence of random seeds on result stability. Moreover, these metrics conceal potential instabilities in individual predictions and in the organization of embedding spaces. In this work, we conduct a systematic stability analysis of multiple KGEMs across several datasets. We find that high-performance models actually produce divergent predictions at the triple level and highly variable embedding spaces. By isolating stochastic factors (i.e., initialization, triple ordering, negative sampling, dropout, hardware), we show that each independently induces instability of comparable magnitude. Furthermore, for a given model, hyperparameter configurations with better MRR are not guaranteed to be more stable. Moreover, voting, albeit a known remediation mechanism, only provides a limited enhancement of stability. These findings highlight critical limitations of current benchmarking protocols, and raise concerns about the reliability of KGEMs for knowledge graph completion.
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.
We propose MABLE (Masked Autoencoding with Bi-Lipschitz Decoding for Embeddings and Graph Metric Learning), a self-supervised framework for learning node and graph embeddings from large, heterogeneous graphs, demonstrated here on geospatial mineral-exploration data. MABLE combines masked reconstruction with fixed cosine-similarity losses that align matched augmented views while keeping unpaired embeddings well spread. A bi-Lipschitz feature decoder ties a low-dimensional reconstruction component of each node embedding to feature similarity, while matched-node consistency shapes the remaining context used by graph pooling. Lipschitz-controlled pooling helps stabilize graph-level representations under perturbations of retained node embeddings, while augmentation alignment trains robustness to masking, node dropping, and sampling variation. Across local copper and regional Arabian Shield studies, MABLE embeddings provide complementary downstream signal and produce coherent embedding-derived layers for hypothesis generation without learned discriminators or hard-negative selection.