What question did this study set out to answer?

Develop a computationally efficient and numerically stable framework for gradient flows in probability distribution spaces using the sliced-Wasserstein metric.

October 21, 2021Open Access

Efficient Gradient Flows in Sliced-Wasserstein Space

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Authors

CBClément BonetÉcole Polytechnique NCNicolas CourtyUniversité Paris-Sud FSFrançois SeptierCentre National de la Recherche Scientifique

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Implication

Computational study demonstrates scalable probability measure optimization in high dimensions, indicating enhanced computational efficiency and stability over standard Wasserstein schemes.

Key Points

Develop a computationally efficient and numerically stable framework for gradient flows in probability distribution spaces using the sliced-Wasserstein metric.
Formulated gradient flows in the space of probability measures equipped with the sliced-Wasserstein distance rather than the classical Wasserstein metric.
Leveraged the closed-form differentiable approximation of the sliced-Wasserstein metric to parameterize evolving densities using general generative models.
Alleviated the computational bottlenecks and instability inherent to nested Jordan-Kinderlehrer-Otto optimization and input convex neural network approximations.
Achieved tractable and flexible gradient flow computation across high-dimensional probability spaces.

Cite This Study

Bonet et al. (2021) studied this question.

synapsesocial.com/papers/6a11c22be2cb0ccec0c90832 https://doi.org/10.48550/arxiv.2110.10972

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Implication

Computational study demonstrates scalable probability measure optimization in high dimensions, indicating enhanced computational efficiency and stability over standard Wasserstein schemes.

Efficient Gradient Flows in Sliced-Wasserstein Space

Discussion

Member takes

Implication

Key Points

Cite This Study

Efficient Gradient Flows in Sliced-Wasserstein Space

Discussion

Member takes

Implication

Key Points

Cite This Study

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