Derives the cold Sinkhorn limiting dynamics as tau approaches zero, proving finite-time convergence to unregularized OT and improved O(tau^{-1}) iteration complexity for dual suboptimality.
Scaling Algorithms for Unbalanced Transport Problems
7 Pith papers cite this work. Polarity classification is still indexing.
7
Pith papers citing it
abstract
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for many applications to be able to compute some sort of relaxed transportation between arbitrary positive measures. A generic class of such "unbalanced" optimal transport problems has been recently proposed by several authors. In this paper, we show how to extend the, now classical, entropic regularization scheme to these unbalanced problems. This gives rise to fast, highly parallelizable algorithms that operate by performing only diagonal scaling (i.e. pointwise multiplications) of the transportation couplings. They are generalizations of the celebrated Sinkhorn algorithm. We show how these methods can be used to solve unbalanced transport, unbalanced gradient flows, and to compute unbalanced barycenters. We showcase applications to 2-D shape modification, color transfer, and growth models.
representative citing papers
Proves sharp O(1/k) rate for Sinkhorn via local bipartite graph analysis of positive-mass edges, bootstrapped from prior almost-sharp global bound.
OTF-CBM replaces static cosine similarity in vision-language CBMs with data-driven optimal transport flow to improve concept alignment, accuracy, and faithfulness.
TransSplat formulates language-driven 3D Gaussian Splatting editing as a multi-view unbalanced semantic transport problem, achieving better cross-view consistency and local editing precision than prior fusion-based methods on 8 benchmark scenes.
TransSplat uses unbalanced semantic transport to match edited 2D evidence with 3D Gaussians and recover a shared 3D edit field, yielding better local accuracy and structural consistency than prior view-consistency methods.
A semi-balanced optimal transport framework with column-capacity constraints for consistent multi-view stylization of 3D Gaussian Splatting.
USIGAN generates pathologically consistent virtual IHC images from weakly paired H&E images by using unbalanced optimal transport to mitigate spatial heterogeneity and adding UOT-CTM and PC-SCM mechanisms for correlation consistency.
citing papers explorer
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Effective dynamics of the Sinkhorn algorithm in the regime of low entropy regularization
Derives the cold Sinkhorn limiting dynamics as tau approaches zero, proving finite-time convergence to unregularized OT and improved O(tau^{-1}) iteration complexity for dual suboptimality.
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Sharp $O(1/k)$ convergence rate for the Sinkhorn algorithm via a local analysis
Proves sharp O(1/k) rate for Sinkhorn via local bipartite graph analysis of positive-mass edges, bootstrapped from prior almost-sharp global bound.
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Bridging Vision and Language Concepts through Optimal Transport Semantic Flow
OTF-CBM replaces static cosine similarity in vision-language CBMs with data-driven optimal transport flow to improve concept alignment, accuracy, and faithfulness.
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RF-HiT: Rectified Flow Hierarchical Transformer for General Medical Image Segmentation
TransSplat formulates language-driven 3D Gaussian Splatting editing as a multi-view unbalanced semantic transport problem, achieving better cross-view consistency and local editing precision than prior fusion-based methods on 8 benchmark scenes.
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TransSplat: Unbalanced Semantic Transport for Language-Driven 3DGS Editing
TransSplat uses unbalanced semantic transport to match edited 2D evidence with 3D Gaussians and recover a shared 3D edit field, yielding better local accuracy and structural consistency than prior view-consistency methods.
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Capacity-Controlled Multi-View Stylization of 3D Gaussian Splatting
A semi-balanced optimal transport framework with column-capacity constraints for consistent multi-view stylization of 3D Gaussian Splatting.
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USIGAN: Unbalanced Self-Information Feature Transport for Weakly Paired Image IHC Virtual Staining
USIGAN generates pathologically consistent virtual IHC images from weakly paired H&E images by using unbalanced optimal transport to mitigate spatial heterogeneity and adding UOT-CTM and PC-SCM mechanisms for correlation consistency.