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The Gromov–Wasserstein Distance Between Spheres.

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Title: The Gromov–Wasserstein Distance Between Spheres.
Authors: Arya, Shreya1 (AUTHOR) smarya@upenn.edu, Auddy, Arnab2 (AUTHOR) auddy.1@osu.edu, Clark, Ranthony A.3 (AUTHOR) ranthony.clark@duke.edu, Lim, Sunhyuk4 (AUTHOR) lsh3109@skku.edu, Mémoli, Facundo5 (AUTHOR) facundo.memoli@gmail.com, Packer, Daniel5 (AUTHOR) daniel.the.packer@gmail.com
Source: Foundations of Computational Mathematics. Feb2026, Vol. 26 Issue 1, p75-130. 56p.
Subjects: Spheres, Euclidean distance, Machine learning, Data science, Metric spaces, Probability measures
Abstract: The Gromov–Wasserstein distance—a generalization of the usual Wasserstein distance—permits comparing probability measures defined on possibly different metric spaces. Recently, this notion of distance has found several applications in Data Science and in Machine Learning. With the goal of aiding both the interpretability of dissimilarity measures computed through the Gromov–Wasserstein distance and the assessment of the approximation quality of computational techniques designed to estimate the Gromov–Wasserstein distance, we determine the precise value of a certain variant of the Gromov–Wasserstein distance between unit spheres of different dimensions. Indeed, we consider a two-parameter family { d GW p , q } p , q = 1 ∞ of Gromov–Wasserstein distances between metric measure spaces. By exploiting a suitable interaction between specific values of the parameters p and q and the metric of the underlying spaces, we are able to determine the exact value of the distance d GW 4 , 2 between all pairs of unit spheres of different dimensions endowed with their Euclidean distance and their uniform measure. [ABSTRACT FROM AUTHOR]
Copyright of Foundations of Computational Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: The Gromov–Wasserstein Distance Between Spheres.
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  Data: <searchLink fieldCode="AR" term="%22Arya%2C+Shreya%22">Arya, Shreya</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> smarya@upenn.edu</i><br /><searchLink fieldCode="AR" term="%22Auddy%2C+Arnab%22">Auddy, Arnab</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> auddy.1@osu.edu</i><br /><searchLink fieldCode="AR" term="%22Clark%2C+Ranthony+A%2E%22">Clark, Ranthony A.</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> ranthony.clark@duke.edu</i><br /><searchLink fieldCode="AR" term="%22Lim%2C+Sunhyuk%22">Lim, Sunhyuk</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> lsh3109@skku.edu</i><br /><searchLink fieldCode="AR" term="%22Mémoli%2C+Facundo%22">Mémoli, Facundo</searchLink><relatesTo>5</relatesTo> (AUTHOR)<i> facundo.memoli@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Packer%2C+Daniel%22">Packer, Daniel</searchLink><relatesTo>5</relatesTo> (AUTHOR)<i> daniel.the.packer@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Foundations+of+Computational+Mathematics%22">Foundations of Computational Mathematics</searchLink>. Feb2026, Vol. 26 Issue 1, p75-130. 56p.
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  Data: <searchLink fieldCode="DE" term="%22Spheres%22">Spheres</searchLink><br /><searchLink fieldCode="DE" term="%22Euclidean+distance%22">Euclidean distance</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink><br /><searchLink fieldCode="DE" term="%22Data+science%22">Data science</searchLink><br /><searchLink fieldCode="DE" term="%22Metric+spaces%22">Metric spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+measures%22">Probability measures</searchLink>
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  Data: The Gromov–Wasserstein distance—a generalization of the usual Wasserstein distance—permits comparing probability measures defined on possibly different metric spaces. Recently, this notion of distance has found several applications in Data Science and in Machine Learning. With the goal of aiding both the interpretability of dissimilarity measures computed through the Gromov–Wasserstein distance and the assessment of the approximation quality of computational techniques designed to estimate the Gromov–Wasserstein distance, we determine the precise value of a certain variant of the Gromov–Wasserstein distance between unit spheres of different dimensions. Indeed, we consider a two-parameter family { d GW p , q } p , q = 1 ∞ of Gromov–Wasserstein distances between metric measure spaces. By exploiting a suitable interaction between specific values of the parameters p and q and the metric of the underlying spaces, we are able to determine the exact value of the distance d GW 4 , 2 between all pairs of unit spheres of different dimensions endowed with their Euclidean distance and their uniform measure. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Foundations of Computational Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Machine learning
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              Text: Feb2026
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