Dear Colleagues,

Artificial neural networks (ANN) represent a hot, fast-growing research field with a large impact on many application areas, such as computer vision, audio and video processing, bioinformatics, data science, pattern recognition, and natural language processing (to mention only a few). In spite of some long-established mathematical results on approximation and modeling capabilities of traditional ANN architectures (in particular, shallow ANNs), the theoretical understanding of the behavior and of the properties of complex or quantum ANNs (including very deep multilayer ANNs, or recurrent neural networks) is still limited. In recent years, the principles and methodologies of several mathematical disciplines have been proposed for the theoretical analysis of ANN architectures, dynamics, and learning. Such disciplines include approximation theory, complexity theory, information theory, as well as the study of von Neumann entropy in quantum ANNs. The purpose of this Special Issue is to highlight the state of the art of the investigation of ANNs in these contexts.

This Special Issue welcomes original research papers on the analysis of ANNs based on mathematically founded methods in general. Review articles describing the current state of the art of ANNs in the aforementioned contexts are highly encouraged. All submissions to this Special Issue must include substantial theoretical aspects of ANN research.

Dr. Friedhelm Schwenker
Dr. Edmondo Trentin
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 submissions that pass pre-check are 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 2600 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.

• ANN architectures and learning in approximation and complexity theories
• Cost functions and constraints in information-theoretic learning algorithms for ANNs
• Complexity of deep, recurrent, or quantum ANN learning
• Information-theoretic principles for sampling and feature extraction
• Analysis of learning based on information-theoretic methods (e.g., information bottleneck approach) in deep, recurrent, or quantum ANNs
• Applications of ANNs based on information-theoretic principles or quantum computing
• Theoretical advances in quantum ANNs