A Unified Dual Method for Matching Problems

arXiv:2609.39339 · cs.CG, stat.ML · Submitted 2026-09-30 · Read on arXiv

cs.CG, stat.ML

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Embeddings — 44× in this paper · explained in 2 episodes
• Accuracy — 22× in this paper · explained in 1 episode
• Optimal Transport — 21× in this paper · explained in 5 episodes
• Hilbert Space — 11× in this paper · explained in 2 episodes
• Regularization — 11× in this paper · explained in 3 episodes
• Alignment — 6× in this paper · explained in 1 episode
• Convergence Guarantees — 5× in this paper · explained in 3 episodes
• Point Clouds — 5× in this paper · explained in 2 episodes
• Sparsity — 5× in this paper · explained in 4 episodes
• Wasserstein Distance — 5× in this paper · explained in 4 episodes
• ACM Transactions on Graphics — 3× in this paper
• Generative AI — 3× in this paper · explained in 2 episodes
• Lyapunov function — 2× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Adaptive Gradient Methods — 1× in this paper · explained in 1 episode
• Alternating Minimization — 1× in this paper · explained in 1 episode
• Clustering — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Cosine Similarity — 1× in this paper · explained in 3 episodes
• Kernel decomposition — 1× in this paper · explained in 2 episodes
• Local Optimization — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Modularity — 1× in this paper · explained in 9 episodes
• Optimal Transport (OT) — 1× in this paper · explained in 4 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Word Translation Without Parallel Data
• Fast and stable randomized low-rank matrix approximation
• FlashSinkhorn: IO-Aware Entropic Optimal Transport on GPU

Related papers

• It's the Geometry, Not the Model: Effective Rank and Subspace Alignment in Functional Connectivity Classification
• Exact and Approximate Range Queries in Ball Mapper
• The optimal-transport cartogram: world population as a Brenier map
• Low-Dimensional Embeddings for Gaussian Kernels on Manifolds
• Direct Topology Tracking in Continuous Implicit Models
• A Sub-4 Approximation for Fair k-Means