Research map / Learning theory and algorithms / Optimal transport
Asymptotics of smoothed Wasserstein distances in the small noise regime
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Require the optimal plan to be unique with positive robustness | Gaussian-smoothed OT on discrete measures · Small noise, σ < σ* | W2 approximation gap rate: σ versus e^{-c/σ^2} | Helped |
| Increase noise beyond the robustness threshold σ* | Gaussian-smoothed OT with a unique robust perfect matching · σ ≥ σ* | Squared W2 approximation gap: σ e^{-cσ*^2/σ^2} | Hurt |
| Have an optimal plan that is not unique and a perfect matching | Gaussian-smoothed OT on discrete measures · σ ∈ (0, c0) | Squared W2 approximation gap: σ | Hurt |
| Keep the smoothing kernel supported within the robustness radius R(Γ) | A unique robust optimal transport plan · Noise supported on B(0, σ*) | W2 distance: W2(μ, ν) = W2(μ * Q, ν * Q) | No clear effect |
Closest papers by meaning
- Scalable Approximation Algorithms for $p$-Wasserstein Distance and Its Variants (ICML 2025 · similarity 0.89)
- Quantifying the noise sensitivity of the Wasserstein metric for images (ICML 2026 · similarity 0.88)
- A Combinatorial Algorithm for the Semi-Discrete Optimal Transport Problem (NeurIPS 2024 · similarity 0.85)
- Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysis (ICML 2025 · similarity 0.85)
- Continuous-time Riemannian SGD and SVRG Flows on Wasserstein Probabilistic Space (NeurIPS 2025 · similarity 0.85)
- Sharp Optimality of Simple, Plug-in Estimation of the Fisher Information of a Smoothed Density (ICML 2025 · similarity 0.85)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.