Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach
Authors: Federico Lopez, Beatrice Pozzetti, Steve Trettel, Michael Strube, Anna Wienhard
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate the representation capacities of the Siegel spaces for the task of graph reconstruction on real and synthetic datasets. We further demonstrate its applicability on two downstream tasks, recommender systems and node classification. |
| Researcher Affiliation | Academia | 1Heidelberg Institute for Theoretical Studies, Heidelberg, Germany 2Mathematical Institute, Heidelberg University, Heidelberg, Germany 3Department of Mathematics, Stanford University, California, USA. |
| Pseudocode | Yes | Algorithm 1 Computing Distances; Algorithm 2 Computing Riemannian Gradient |
| Open Source Code | Yes | Code available at https://github.com/ fedelopez77/sympa. |
| Open Datasets | Yes | We compare the models on two road networks, namely USCA312 of distances between North American cities and EUROROAD between European cities, BIO-DISEASOME, a network of human disorders and diseases with reference to their genetic origins (Goh et al., 2007), a graph of computer science Ph.D. advisor-advisee relationships (Nooy et al., 2011), and a dense social network from Facebook (Mc Auley & Leskovec, 2012). |
| Dataset Splits | Yes | To generate evaluation splits, the penultimate and last item the user has interacted with are withheld as dev and test set respectively. |
| Hardware Specification | No | The paper does not provide specific details on the hardware used for running experiments (e.g., GPU/CPU models, memory). |
| Software Dependencies | No | The paper mentions "Geoopt (Kochurov et al., 2020)" and implies the use of "Pytorch" in references, but does not provide specific version numbers for these or other software dependencies. |
| Experiment Setup | Yes | We initialize the matrix embeddings in the Siegel upper half space by adding small symmetric perturbations to the matrix basepoint i Id. In all cases we optimize with RSGD (Bonnabel, 2011) and report the average of 5 runs. We experiment with the loss proposed in Gu et al. (2019), which minimizes the relation between the distance in the space, compared to the distance in the graph, and captures the average distortion. |