mlsanityData to 14 Oct 2026

Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysis

arXiv 2502.06525 ↗First posted 10 Feb 2025stat.ML cs.LGcited by 3

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Abstract (arXiv)

In this paper, we investigate the properties of the Sliced Wasserstein Distance (SW) when employed as an objective functional. The SW metric has gained significant interest in the optimal transport and machine learning literature, due to its ability to capture intricate geometric properties of probability distributions while remaining computationally tractable, making it a valuable tool for various applications, including generative modeling and domain adaptation. Our study aims to provide a rigorous analysis of the critical points arising from the optimization of the SW objective. By computing explicit perturbations, we establish that stable critical points of SW cannot concentrate on segments. This stability analysis is crucial for understanding the behaviour of optimization algorithms for models trained using the SW objective. Furthermore, we investigate the properties of the SW objective, shedding light on the existence and convergence behavior of critical points. We illustrate our theoretical results through numerical experiments.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 34 of its 48 references that are in the map. First posted on arXiv 10 Feb 2025.

Builds on

34 of 48 references.

References · 34

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22 more
  1. 2021Variational Wasserstein gradient flowcited by 53
  2. 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Sliced Wasserstein Steering between Gaussian Measurescited by 1
  2. 2026Convergence of empirical subgradients for optimal transport-based objectivescited by 0
  3. 2026Distribution Steering via Sliced Optimal Transport Controlcited by 0