Optimal Transport
optimal-transport-1054bdf4·3 events·first seen 22d agoAliases: Optimal Transport
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Optimal Mixture Transport (OMT): Biconvex Formulation for Scalable, Stable Optimal Transport
This paper introduces Optimal Mixture Transport (OMT), a framework that reformulates optimal transport between probability distributions as a strictly biconvex optimization problem with a provably unique global minimizer. By operating at the level of mixture components (modeled as exponential-family distributions) rather than individual samples, OMT decouples computational complexity from sample size. The authors provide theoretical stability guarantees showing bounded perturbations yield bounded changes in transport plans, and validate the approach on image data and large-scale single-cell RNA sequencing datasets.
Global Convergence Theory for Wasserstein Policy Gradient in Entropy-Regularized RL
This paper establishes the first global convergence theory for Wasserstein Policy Gradient (WPG), a continuous-control RL optimization method that uses optimal-transport geometry over action distributions. The authors show that the Bellman recursion structure of entropy-regularized RL induces a Polyak–Łojasiewicz (PL) geometry that substitutes for classical convexity, enabling global convergence analysis. Key technical contributions include a statewise KL representation of the soft Bellman residual, a Bellman resolvent identity linking value improvement to relative Fisher information, and a uniform log-Sobolev inequality for the evolving Gibbs policy family. The result yields geometric contraction up to discretization bias, providing theoretical grounding for WPG in continuous-action settings.
AREA: Attribute Extraction and Aggregation for CLIP-Based Class-Incremental Learning
AREA is a new method for CLIP-based Class-Incremental Learning (CIL) that decomposes the classification process into attribute extraction and aggregation stages to combat catastrophic forgetting. Extraction is stabilized by anchoring visual and textual attributes on a hyperspherical embedding space via principal geodesic analysis, while aggregation uses lightweight task-specific experts regularized by a variational information bottleneck. Inference employs optimal transport routing over task attribute manifolds. The method is reported to consistently outperform state-of-the-art CIL approaches and is accepted at ICML 2026.