Energy-Guided Continuous Entropic Barycenter Estimation for General Costs
Authors: Alexander Kolesov, Petr Mokrov, Igor Udovichenko, Milena Gazdieva, Gudmund Pammer, Anastasis Kratsios, Evgeny Burnaev, Aleksandr Korotin
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | For validation, we consider several low-dimensional scenarios and image-space setups, including non-Euclidean cost functions. Furthermore, we investigate the practical task of learning the barycenter on an image manifold generated by a pretrained generative model, opening up new directions for real-world applications. Our code is available at https://github.com/justkolesov/Energy Guided Barycenters. |
| Researcher Affiliation | Academia | Alexander Kolesov Skolkovo Institute of Science and Technology Artificial Intelligence Research Institute Moscow, Russia a.kolesov@skoltech.ru Petr Mokrov & Igor Udovichenko Skolkovo Institute of Science and Technology Moscow, Russia {p.mokrov, i.udovichenko}@skoltech.ru Milena Gazdieva Skolkovo Institute of Science and Technology Artificial Intelligence Research Institute Moscow, Russia m.gazdieva@skoltech.ru Gudmund Pammer Graz University of Technology Graz, Austria gudmund.pammer@tugraz.at Anastasis Kratsios Vector Institute, Mc Master University Ontario, Canada kratsioa@mcmaster.ca Evgeny Burnaev & Alexander Korotin Skolkovo Institute of Science and Technology Artificial Intelligence Research Institute Moscow, Russia {e.burnaev, a.korotin}@skoltech.ru |
| Pseudocode | Yes | Algorithm 1: EOT barycenters via Energy-Based Modelling |
| Open Source Code | Yes | Our code is available at https://github.com/justkolesov/Energy Guided Barycenters. |
| Open Datasets | Yes | A classic experiment considered in the continuous barycenter literature [32, 55, 82, 17] is averaging of distributions of MNIST 0/1 digits with weights ( 1 2) in the grayscale image space X1 = X2 = Y = [ 1, 1]32 32. In [55], the authors developed a theoretically grounded methodology for finding probability distributions whose unregularized ℓ2 barycenter is known by construction. Based on the Celeb A faces dataset [73], they constructed an Ave, celeba! dataset containing 3 degraded subsets of faces. |
| Dataset Splits | No | The paper mentions training samples and out-of-sample estimation but does not provide specific details on validation dataset splits (percentages, counts, or predefined splits). |
| Hardware Specification | Yes | Reproducing the most challenging experiments ( 5.2, 5.3) requires less than 12 hours on a single Tesla V100 GPU. The hardware is a single V100 gpu. |
| Software Dependencies | No | The paper mentions 'Py Torch framework' for the solver and uses 'ULA' (an algorithm), and links to 'stylegan2-ada-pytorch' code. However, it does not provide specific version numbers for PyTorch or other software dependencies. |
| Experiment Setup | Yes | The hyperparameters of our solver are summarized in Table 4. Some hyperparameters, e.g., L, S, iter, are chosen primarily from time complexity reasons. Typically, the increase in these numbers positively affects the quality of the recovered solutions, see, e.g., [42, Appendix E, Table 16]. However, to reduce the computational burden, we report the figures which we found to be reasonable. Working with the manifold-constraint setup, we parameterize each gθk(z) in our solver as hθk G(z), where G is a pre-trained (frozen) Style GAN and hθk is a neural network with the Res Net architecture. We empirically found that this strategy provides better results than a direct MLP parameterization for the function gθk(z). |