Abstract
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.
Data and code availability
We provide all code used to load and create the datasets and to reproduce our results under https://github.com/dess-mannheim/dimpact
Funding
Open Access funding enabled and organized by Projekt DEAL. This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Grant No. 453349072. The authors acknowledge support by the state of Baden-Württemberg through bwHPC and DFG through grant INST 35/1597–1 FUGG.
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Schumacher, T., Reichelt, S. & Strohmaier, M. The impact of dimensionality on the stability of node embeddings. Appl Netw Sci (2026). https://doi.org/10.1007/s41109-026-00830-2
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DOI: https://doi.org/10.1007/s41109-026-00830-2
Facts Only
* T. Schumacher, S. Reichelt, and M. Strohmaier are the authors.
* The study analyzes five node embedding methods: ASNE, DGI, GraphSAGE, node2vec, and VERSE.
* Stability is evaluated from representational and functional perspectives.
* Analysis covers varying embedding dimensions, datasets, and repeated training runs.
* node2vec and ASNE stability generally increases with higher dimensions.
* GraphSAGE and VERSE stability is non-monotonic or decreases with higher dimensions.
* High stability dimensions do not always coincide with dimensions yielding strongest downstream performance.
* Research is supported by the Deutsche Forschungsgemeinschaft (DFG) Grant No. 453349072.
* Additional support provided by the state of Baden-Württemberg via bwHPC and DFG grant INST 35/1597–1 FUGG.
* Code and dataset loading tools are available at https://github.com/dess-mannheim/dimpact
* The work is published in Applied Network Science (2026).
Executive Summary
Node embedding methods can produce inconsistent representations and downstream predictions across repeated training runs, even when hyperparameters and data remain identical. The stability of these embeddings is significantly influenced by the dimensionality of the embedding space, though the nature of this impact varies by method.
Certain algorithms, such as node2vec and ASNE, generally exhibit increased stability as dimensionality increases. Conversely, GraphSAGE and VERSE often demonstrate non-monotonic behavior or a decrease in stability at higher dimensions. Crucially, there is a decoupling between stability and predictive power; dimensions that provide the most stable embeddings do not necessarily result in the highest downstream performance. This indicates a complex trade-off between the reliability of the representation and its functional utility.
Full Take
This research employs a systematic empirical approach to address the "instability" problem in graph machine learning. By testing across five diverse architectures, the study avoids the trap of over-generalizing a single model's behavior. However, a peer reviewer would note that while the abstract claims a "broad range" of datasets, the specific number and nature of these datasets (e.g., sparsity, scale, homophily) are not detailed here, which is critical since graph topology often dictates embedding behavior.
The central finding—that stability and performance are not perfectly correlated—challenges the implicit assumption that a more "reliable" or "stable" model is inherently a "better" one. This suggests that some level of stochasticity or sensitivity in lower dimensions might actually be capturing nuanced structural information that contributes to predictive power, even if it makes the model less reproducible.
If these findings hold, practitioners can no longer treat dimensionality as a simple "more is better" or "less is better" hyperparameter. Instead, the choice of dimension must be a deliberate trade-off between the need for reproducible results (stability) and the need for maximum accuracy (performance).
To strengthen these claims, follow-up research should investigate *why* certain architectures (like GraphSAGE) lose stability as dimensions increase. Is this a result of overfitting to noise in higher-dimensional spaces, or an inherent property of the aggregation mechanism?
Bridge Questions:
1. At what specific threshold does the trade-off between stability and performance become critical for production-grade AI?
2. Would incorporating ensemble averaging across repeated runs mitigate instability without sacrificing the performance gains of lower-dimensional embeddings?