English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Many problems in machine learning can be formulated as solvingentropy-regularized optimal transport on the space of probability measures. Thecanonical approach involves the Sinkhorn iterates, renowned for their richmathematical properties. Recently, the Sinkhorn algorithm has been recastwithin the mirror descent framework, thus benefiting from classicaloptimization theory insights. Here, we build upon this result by introducing acontinuous-time analogue of the Sinkhorn algorithm. This perspective allows usto derive novel variants of Sinkhorn schemes that are robust to noise and bias.Moreover, our continuous-time dynamics not only generalize but also offer aunified perspective on several recently discovered dynamics in machine learningand mathematics, such as the "Wasserstein mirror flow" of (Deb et al. 2023) orthe "mean-field Schr\"odinger equation" of (Claisse et al. 2023).

Sinkhorn Flow: A Continuous-Time Framework for Understanding and Generalizing the Sinkhorn Algorithm