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 [1].
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... |