Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Gromov-Wasserstein Averaging of Kernel and Distance Matrices
Authors: Gabriel Peyré, Marco Cuturi, Justin Solomon
ICML 2016 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate its application to the computation of shape barycenters and to the prediction of energy levels from molecular configurations in quantum chemistry. |
| Researcher Affiliation | Academia | Gabriel Peyr e EMAIL CNRS and Univ. Paris-Dauphine, Pl. du M. De Lattre De Tassigny, 75775 Paris 16, FRANCE Marco Cuturi EMAIL Kyoto University, 36-1 Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, JAPAN Justin Solomon EMAIL Massachusetts Institute of Technology, Cambridge, MA 02139, USA |
| Pseudocode | Yes | Algorithm 1 Computation of GWε barycenters. |
| Open Source Code | Yes | The code to reproduce the results of this paper is available online.1 |
| Open Datasets | Yes | In this experiment, we extract 500 point clouds of handwritten digits from the dataset (Le Cun et al., 1998), rotated arbitrarily in the plane... qm7 dataset of organic 7165 molecules |
| Dataset Splits | Yes | (Hansen et al., 2013, Table 3) provide out-of-sample mean absolute error (MAE) predictions for several techniques using 5 fold cross-validation. |
| Hardware Specification | No | The paper does not specify the hardware used for running experiments. |
| Software Dependencies | No | The paper mentions algorithms like Sinkhorn iterations and k-means but does not specify software dependencies with version numbers (e.g., Python, PyTorch, specific libraries). |
| Experiment Setup | Yes | We represent each digit as a symmetric Euclidean distance matrix and optimize for a 500 x 500 barycenter using Algorithm 1 (uniform weights, ε = 1 10 3)... We then cluster the point clouds by representing them as pairwise distance matrices and applying the k-means algorithm (k = 5), with k-means++ initialization (Arthur & Vassilvitskii, 2007)... Using a 3-nearest neighbor regression approach... |