Learning Mixed-Curvature Representations in Product Spaces
Authors: Albert Gu, Frederic Sala, Beliz Gunel, Christopher Ré
ICLR 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate the proposed approach, comparing the representation quality of synthetic graphs and real datasets among different embedding spaces by measuring the reconstruction fidelity (through average distortion and m AP). |
| Researcher Affiliation | Academia | Albert Gu, Frederic Sala, Beliz Gunel & Christopher R e Computer Science Department Stanford University Stanford, CA 94305 {albertgu,fredsala,bgunel}@stanford.edu, chrismre@cs.stanford.edu |
| Pseudocode | Yes | Algorithm 1 R-SGD in products |
| Open Source Code | No | The paper does not provide an explicit statement about releasing source code or a link to a repository for the methodology described. |
| Open Datasets | Yes | Datasets We examine synthetic datasets trees, cycles, the ring of trees shown in Figure 1, confirming that each matches its theoretically optimal embedding space. We then compare on several real-world datasets with describable structure, including the USCA312 dataset of distances between North American cities (Burkardt); a tree-like graph of computer science Ph.D. advisor-advisee relationships (De Nooy et al., 2011) reported in previous hyperbolics work (Sala et al., 2018); a powergrid distribution network with backbone structure (Watts & Strogatz, 1998); and a dense social network from Facebook (Mc Auley & Leskovec, 2012). ... We use the standard skip-gram model (Mikolov et al., 2013) ... The datasets used for similarity (WS-353, Simlex-999, MEN) and analogy (Google) are also identical to the previous setup. |
| Dataset Splits | No | The paper does not specify exact percentages or sample counts for training, validation, and test splits, nor does it refer to predefined splits with specific citations for all datasets used. |
| Hardware Specification | No | The paper does not specify any particular GPU or CPU models, processor types, or memory details used for running experiments, only mentioning the software framework PyTorch. |
| Software Dependencies | No | The paper mentions software like PyTorch and fastText but does not provide specific version numbers for these or any other ancillary software components, preventing reproducible setup. |
| Experiment Setup | Yes | The loss function (2) was optimized with SGD using minibatches of 65536 edges for the real-world datasets, and ran for 2000 epochs. For the Cities graph, the learning rate was chosen among {0.001, 0.003, 0.01}. For the rest of the datasets, the learning rate was chosen from a grid search among {10, 30, 100, 300, 1000} for each method. ... Each point in the embedding is initialized randomly according to a uniform or Normal distribution in each coordinate with standard deviation 10 3. ... All other hyperparameters are chosen exactly as in as LW, including their numbers for Euclidean embeddings from fast Text. |