Stereographic Spherical Sliced Wasserstein Distances
Authors: Huy Tran, Yikun Bai, Abihith Kothapalli, Ashkan Shahbazi, Xinran Liu, Rocio P Diaz Martin, Soheil Kolouri
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, we evaluate the performance of the proposed metrics and compare them with recent baselines in terms of both speed and accuracy through a wide range of numerical studies, including gradient flows and selfsupervised learning. and 5. Experiments Here, we present key results from our numerical experiments. |
| Researcher Affiliation | Academia | 1Department of Computer Science, Vanderbilt University, Nashville, TN 2Department of Mathematics, Vanderbilt University, Nashville, TN. |
| Pseudocode | Yes | Algorithm 1 S3W Input: {xi}M i=1 µ, {yj}M j=1 ν, L projections, p-th order, ϵ for excluding the ϵ-cap around sn. Initialize: h (injective map), {θl}L l=1 (projections) Compute {ui = h(ϕϵ(xi))} and {vj = h(ϕϵ(yj))} Initialize distance d = 0 for l = 1 to L do Compute ul i = ui, θl , vl j = vj, θl Sort {ul i}, {vl j}, s.t ul πl[i] ul πl[i+1], vl π l[j] vl π l[j+1] d = d + 1 L PM i=1 |ul πl[i] vl π l[i]|p end for Return d 1 p |
| Open Source Code | Yes | Our code is available at https://github.com/mint-vu/s3wd. |
| Open Datasets | Yes | We run our experiments on CIFAR-10 using a Res Net18 encoder. and Details about the network architectures and results on the MNIST benchmark can be found in the appendix Section I.9. and Our focus is on the three datasets introduced by (Mathieu & Nickel, 2020), representing the Earth s surface as a perfect spherical manifold: Earthquake (NOAA, 2022), Flood (Brakenridge, 2017), and Fire (EOSDIS, 2020). |
| Dataset Splits | No | The paper mentions training on CIFAR-10 and MNIST datasets, and reports test accuracy, but does not explicitly provide details about validation dataset splits or methodology for creating such splits. For Earth datasets, Table 5 shows Train and Test splits, but no validation split is mentioned. |
| Hardware Specification | Yes | All our experiments were executed on a Linux server with an AMD EPYC 7713 64-Core Processor, 8 32GB DIMM DDR4, 3200 MHz, and a NVIDIA RTX A6000 GPU. |
| Software Dependencies | No | The paper mentions the "Geo Torch library (Lezcano-Casado, 2019)" and the "Python OT library (Flamary et al., 2021)", but it does not provide specific version numbers for these or other key software dependencies like programming languages, machine learning frameworks, or operating systems. |
| Experiment Setup | Yes | We optimize over 500 gradient steps using the Adam Optimizer (learning rate of γ = 0.01 for full-batch and 0.001 for mini-batch) for 10 in dependent runs. We report both qualitative and quantitative results (NLL, W2); the latter comes with mean and standard deviation. and The models are pretrained for 200 epochs with minibatch SGD (momentum 0.9, weight decay 0.001, initial learning rate 0.05). We select the batch size to be 512 samples and use the standard random augmentation set consisting of random crop, horizontal flipping, color jittering, and gray scale transformation, as done in (Bonet et al., 2023a; Wang & Isola, 2020). |