Mathematical Perspectives on Generalization and Optimization in Machine Learning
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".
Deadline for manuscript submissions: 31 October 2026 | Viewed by 224
Special Issue Editor
Special Issue Information
Dear Colleagues,
Machine learning systems have reached an impressive level of performance in a wide range of applications, often well beyond what was expected just a few years ago. At the same time, our mathematical understanding of how these systems work—and under which conditions they fail—is still fragmentary. Questions related to generalization, optimization behavior, and robustness are frequently addressed empirically; however, a unified and rigorous theoretical picture is still missing. This Special Issue aims to serve as a contribution in that direction.
We invite papers that approach these problems from a mathematical perspective, including studies on generalization properties of deep or stochastic models, analyses of optimization dynamics and implicit regularization, and investigations into the stability and robustness of learning algorithms. Contributions on the mathematical basis of explainable and interpretable AI are also welcome, as are works connecting machine learning to neighboring areas such as information theory or statistical mechanics. Many modern learning settings—overparameterized networks, stochastic components in training, ensemble methods, or reinforcement learning—do not fit neatly into classical assumptions, and understanding them requires new tools.
The objective of this Special Issue is not only to present new theoretical results but also to encourage work that helps clarify the mechanisms behind contemporary learning methods. We are particularly interested in contributions that combine mathematical rigor with insight into practical behavior, helping to explain when current approaches are reliable and how they might be improved.
Dr. Carlo Metta
Guest Editor
Manuscript Submission Information
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Keywords
- machine learning theory
- generalization
- optimization
- mathematical foundations of AI
- explainable artificial intelligence
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