Mathematics and Deep Learning
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".
Deadline for manuscript submissions: closed (31 May 2024) | Viewed by 2666
Special Issue Editor
Special Issue Information
Dear Colleagues,
Deep Learning (DL) is a fast-growing area with a potentially enormous and transformative impact. However, alongside this explosive growth, the efficiency and limitations of deep learning raise profound questions in statistics, probability, optimization, harmonic analysis, geometry, and scientific computing. The underlying mathematics remain mostly not understood, limiting the robustness and validation of applications in critical domains such as autonomous driving, medicine, or hard sciences.
As a data-driven approach, deep learning is built upon the pillars of mathematics and statistics, while there is currently no satisfactorily rigorous mathematical theory for the setup, training, and application performance of deep neural networks. To unlock the next generation of DL, it is important to address both the theoretical development for explainable DL as well as the algorithmic development for trustworthy DL. These will then be linked to the development of DL in a number of key application areas, including image processing, partial differential equations, and AI for science problems.
The main aim of this Special Issue is an interlocked set of theory, modeling, data, and computation. We seek original contributions that discuss the mathematical foundations of the success of recent DL frameworks or highlight emerging applications in mathematics in deep learning.
Dr. Xiaofeng Liu
Guest Editor
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Keywords
- loss function and optimization
- model generalization and adaptation
- partial differential equations (PDEs)-based models
- inverse problems
- uncertainty quantification
- regularization
- approximation of layers
- posterior estimation
- geometry and graphs
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