On the Learning and Learnability of Quasimetrics

Authors: Tongzhou Wang, Phillip Isola

ICLR 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Experiments on random graphs, social graphs, and offline Q-learning demonstrate its effectiveness over many common baselines. Project Page: ssnl.github.io/quasimetric. Code: github.com/Ssn L/poisson_quasimetric_embedding.
Researcher Affiliation Academia Tongzhou Wang MIT CSAIL Phillip Isola MIT CSAIL
Pseudocode Yes Algorithm 1 Random quasipartition of a bounded treewidth graph. Algorithm 2 of (Mémoli et al., 2018).
Open Source Code Yes Code: github.com/Ssn L/poisson_quasimetric_embedding.
Open Datasets Yes We choose the Berkeley-Stanford Web Graph (Leskovec & Krevl, 2014) as the real-wold social graph for evaluation. This graph consists of 685,230 pages as nodes, and 7,600,595 hyperlinks as directed edges. We use 128-dimensional node2vec features (Grover & Leskovec, 2016) and the landmark method (Rizi et al., 2018) to construct a training set of 2,500,000 pairs, and a test set of 150,000 pairs.
Dataset Splits No The paper primarily describes train/test splits, such as “randomly sample the training set, and use the rest as the test set” and “form a test set of 150,000”. It does not explicitly mention a separate validation set for hyperparameter tuning or model selection across all experiments.
Hardware Specification Yes All our experiments run on a single GPU and finish within 3 hours. GPUs we used include NVIDIA 1080, NVIDIA 2080 Ti, NVIDIA 3080 Ti, NVIDIA Titan Xp, NVIDIA Titan RTX, and NVIDIA Titan V.
Software Dependencies No The paper mentions software like “Sci Py (Virtanen et al., 2020)”, “CDFLIB (Burkardt, 2021; Brown et al., 1994)”, and “PyTorch (Paszke et al., 2019)”. However, it does not explicitly state specific version numbers for these software packages, which is required for full reproducibility.
Experiment Setup Yes We use 2048 batch size with the Adam optimizer (Kingma & Ba, 2014), with learning rate decaying according to the cosine schedule without restarting (Loshchilov & Hutter, 2016) starting from 10 4 to 0 over 3000 epochs. All models are optimized w.r.t. MSE on the γ-discounted distances, with γ = 0.9. When running with the triangle inequality regularizer, 683 2048/3 triplets are uniformly sampled at each iteration.