Tree-Sliced Wasserstein Distance: A Geometric Perspective
Authors: Hoang V. Tran, Huyen Trang Pham, Tho Tran Huu, Minh-Khoi Nguyen-Nhat, Thanh Chu, Tam Le, Tan Minh Nguyen
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | By conducting a variety of experiments on gradient flows, image style transfer, and generative models, we illustrate that our proposed approach performs favorably compared to SW and its variants. |
| Researcher Affiliation | Collaboration | 1National University of Singapore 2Movian AI 3The Institute of Statistical Mathematics. Correspondence to: Viet-Hoang Tran <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Sampling (chain-like) tree systems. Input: The number of lines in tree systems k. Sampling x1 U([ 1, 1]d) and θ1 U(Sd 1). for i = 2 to k do Sample ti U([ 1, 1]) and θi U(Sd 1). Compute xi = xi 1 + ti θi 1. end for Return: (x1, θ1), (x2, θ2), . . . , (xk, θk). |
| Open Source Code | No | The paper does not explicitly provide a link to a code repository, nor does it state that the code for the methodology described in this paper is openly available or in supplementary materials. It mentions utilizing adapted source code from previous works for specific tasks, but not its own. |
| Open Datasets | Yes | We first utilize both the Swiss Roll (a non-linear dataset) and 25 Gaussians (a multimodal dataset) as described in (Kolouri et al., 2019). ... deep generative modeling experiments on the non-cropped Celeb A dataset (Krizhevsky, 2009) with image size 64 64, and on the STL-10 dataset (Wang & Tan, 2016) with image size 96 96. ... conducting experiments on the CIFAR-10 dataset (Krizhevsky, 2009). |
| Dataset Splits | No | The paper mentions using datasets like Celeb A, STL-10, and CIFAR-10 for training and evaluation but does not specify how these datasets were split into training, validation, or test sets (e.g., specific percentages or sample counts). It refers to 'all training samples' for FID evaluation but lacks explicit split details. |
| Hardware Specification | Yes | The experiments on gradient flow, color transfer and generative models using generative adversarial networks are conducted on a single NVIDIA A100 GPU. ... The denoising diffusion experiments were conducted parallelly on 2 NVIDIA A100 GPUs |
| Software Dependencies | No | The paper mentions using Adam optimizer (Kingma, 2014) and Pytorch for dataset generation, but does not specify version numbers for these or other key software libraries and dependencies required for reproduction. |
| Experiment Setup | Yes | For TSW-SL, we use L = 25, k = 4 in all experiments, while L = 100 is set for SW and SW-variants, with 100 points generated per distribution across datasets. Following (Mahey et al., 2023), the global learning rate for all baselines is 5e-3. For our methods, we use 5e-3 for the 25-Gaussians and Swiss Roll datasets, and 5e-2 for the high-dimensional Gaussian datasets. We also follow (Mahey et al., 2023) in setting 100 iterations for both Max SW and Max TSW-SL, using a learning rate of 1e-4 for both methods. ... We configured the number of training iterations to 100000 for CIFAR10, STL-10 and 50000 for Celeb A. The generator Gϕ is updated every 5 iteration, while the feature function Tβ undergoes an update each iteration. Across all datasets, we maintain a consistent mini-batch size of 128. We leverage the Adam optimizer (Kingma, 2014) with parameters (β1, β2) = (0, 0.9) for both Gϕ and Tβ with the learning rate 0.0002. ... training our models for 1800 epochs. For TSW, we employed the following hyperparameters: L = 2500, k = 4. For the vanilla SW and its variants, we adhered to the approach outlined in Nguyen et al. (2024b), using L = 10000. |