Shadow Cones: A Generalized Framework for Partial Order Embeddings
Authors: Tao Yu, Toni J.B. Liu, Albert Tseng, Christopher De Sa
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our experiments on datasets of various sizes and hierarchical structures show that shadow cones consistently and significantly outperform existing entailment cone constructions. and Achieve state-of-the-art results on a wide range of graph embedding tasks, lending both empirical and theoretical support to the advantages of all four embedding schemes. and 5 EXPERIMENTS This section showcases shadow cones ability to represent and infer hierarchical relations on four datasets (detailed statistics in Appendix G): MCG (Wang et al., 2015; Wu et al., 2012; Li et al., 2017), Hearst patterns (Hearst, 1992; Le et al., 2019), Word Net Noun (Christiane, 1998), and its Mammal sub-graph. |
| Researcher Affiliation | Academia | Tao Yu , Toni J.B. Liu , Albert Tseng, and Christopher De Sa Cornell University {ty367, jl3499, at676, cmd353}@cornell.edu |
| Pseudocode | No | The paper does not contain any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | Our code is available on github https://github.com/ydtydr/Shadow Cones |
| Open Datasets | Yes | This section showcases shadow cones ability to represent and infer hierarchical relations on four datasets (detailed statistics in Appendix G): MCG (Wang et al., 2015; Wu et al., 2012; Li et al., 2017), Hearst patterns (Hearst, 1992; Le et al., 2019), Word Net Noun (Christiane, 1998), and its Mammal sub-graph. |
| Dataset Splits | Yes | The remaining 10% of non-basic edges are evenly divided between the validation and test sets. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory specifications) used for running experiments. |
| Software Dependencies | No | The paper mentions using "HTorch (Yu et al., 2023) for optimization in various models of hyperbolic space. We use Riemannian SGD for Poincaré half-space model, and Riemannian Adam for Poincaré ball model". However, no specific version numbers are provided for HTorch or the optimizers, which are necessary for reproducibility. |
| Experiment Setup | Yes | For the margin parameters in shadow loss, we use γ2 = 0 consistently for all experiments. We tune γ1 and the learning rate in {0.01, 0.001, 0.0001}. For umbral cones, we tune the source radius r in {0.01, 0.05, 0.1, 0.2, 0.3}, empirically r = 0.05 during training gives the optimal performance when evaluated under a slightly larger radius r = 0.1. For penumbral-half-space cones, we tune the exponentiated height kh in {2, 5, 10, 20}... We set γ3 = 0.0001 consistently for all shadow cones. We use Riemannian SGD for Poincaré half-space model, and Riemannian Adam for Poincaré ball model. and A training batchsize of 16 is used for all datasets and models. |