Formal Analysis of Deep Artificial Neural Networks

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

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