Veronica Lachi
Veronica Lachi is a researcher in the Mobile and Social Computing Lab at Bruno Kessler Foundation in Trento. Her research interests focus on the theoretical properties of Graph Neural Networks, particularly their expressiveness, hierarchical pooling, and temporal GNNs. She obtained a PhD in Artificial Intelligence from the University of Siena under the supervision of Prof. Monica Bianchini. During her PhD, she was a Visiting Researcher at UiT The Arctic University of Tromsø.
Project
Recent advances in graph representation learning have introduced models that leverage hyperbolic space instead of traditional Euclidean spaces [1,2,3,4]. The motivation behind this shift stems from theoretical results which demonstrated that tree-like structures can be embedded in hyperbolic space with arbitrarily low distortion—an advantage that Euclidean space does not provide [5]. However, in [6] it has been shown that Euclidean models with comparable number of parameters can match or even surpass the performance of hyperbolic graph models. This suggests that the benchmark tasks used to justify hyperbolic methods may not be well-suited for distinguishing their benefits from those of standard Euclidean models. In other words, the choice of datasets and evaluation protocols may not accurately reflect the claimed advantages of hyperbolic embeddings. A key issue is the metric used to quantify the hyperbolicity of graph datasets. The widely used δ-hyperbolicity measure characterizes the entire graph structure but does not account for the interplay between node features and connectivity. Moreover, this measure is relatively coarse.
The goal of this project is to refine the evaluation of hyperbolic graph learning models by identifying a more informative metric for assessing dataset hyperbolicity. Specifically, we will (1) identify other metrics which provide a finer geometric characterization of graph structures by incorporating both topology and feature information (an example is Ollivier-Ricci curvature [7]); (2) computing and analyzing this curvature across multiple real-world graph datasets of varying sizes, identifying cases where hyperbolic embeddings are genuinely beneficial; (3) repeat the experiments presented in [5] on the selected datasets.
Beyond this immediate objective, the project has the possibility of extension in future works. A long-term goal is to develop models capable of learning the most appropriate underlying manifold for a given dataset and task, rather than assuming a fixed geometric prior.
[1] Ganea, Octavian, Gary Bécigneul, and Thomas Hofmann. “Hyperbolic neural networks.” Advances in neural information processing systems 31 (2018).
[2] Chami, Ines, et al. “Hyperbolic graph convolutional neural networks.” Advances in neural information processing systems 32 (2019).
[3] Shimizu, Ryohei, Yusuke Mukuta, and Tatsuya Harada. “Hyperbolic neural networks++.” arXiv preprint arXiv:2006.08210 (2020).
[4] Zhang, Yiding, et al. “Lorentzian graph convolutional networks.” Proceedings of the web conference 2021. 2021.
[5] Sarkar, Rik. “Low distortion Delaunay embedding of trees in hyperbolic plane.” International symposium on graph drawing. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011.
[6] Katsman, Isay, and Anna Gilbert. “Shedding Light on Problems with Hyperbolic Graph Learning.” Transactions on Machine Learning Research, 2024.
[7] Lin, Yong, Linyuan Lu, and Shing-Tung Yau. “Ricci curvature of graphs.” Tohoku Mathematical Journal, Second Series 63.4 (2011): 605-627.
