Special Issue "Geometry in Machine Learning"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (30 September 2020).

Special Issue Editors

Prof. Mikhail Belkin
Guest Editor
Department of Computer Science and Engineering, Ohio State University, Columbus, OH 43210, USA
Interests: optimization; machine learning; deep learning
Dr. Varun Jog
Guest Editor
Departments of Electrical & Computer Engineering, University of Wisconsin, Madison, WI 53706, USA
Interests: Information theory; machine learning; convex geometry
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Special Issue Information

Dear Colleagues,

Recent years have seen a surge of interest in developing geometric techniques for analyzing machine learning algorithms. Much of this work is motivated by the need to understand the performance of deep learning-based algorithms that have revolutionized modern machine learning over the past decade. Methods from geometry have been successfully used to gain insight into three crucial aspects of modern machine learning: generalization, robustness, and optimization. Some examples include analyzing the generalization properties of interpolating classifiers, the relation between smoothness and curvature of classification boundaries to the robustness and generalization performance of the classifier, and the impact of parametrization and choice of optimization algorithm on the quality of a learned model. Optimal transport theory, which lies at the intersection of geometry and probability, has found applications in the theoretical analysis of machine learning algorithms and has also been used to propose novel generative models. Other mathematical areas such as differential geometry and information geometry have been applied to investigate learning and optimization on manifolds.

In this Special Issue, we welcome submissions related to the geometry of deep learning, applications of optimal transport, information geometry, and high-dimensional geometry for the theoretical analysis of machine learning algorithms. This is a highly interdisciplinary research topic, and we invite contributions from the mathematics, computer science, and engineering communities. Through this issue, we hope to highlight and strengthen the deep connections between geometry and machine learning.

Prof. Mikhail Belkin
Prof. Varun Jog
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • manifold learning
  • optimal transport
  • differential geometry
  • robust machine learning
  • generalization
  • optimization

Published Papers

There is no accepted submissions to this special issue at this moment.
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