Folding networks, a generalization of recurrent neural networks to tree structured inputs, are investigated as a mechanism to learn regularities on classical symbolic data, for example. The architecture, the training mechanism, and several applications in different areas are explained. After wards a theoretical foundation, proving that the approach is appropriate as a learning mechanism in principle, is presented: Their universal approximation ability is investigated - including several new results for standard recurrent neural networks such as explicit bounds on the required number of...

Das vorliegende Lehrbuch basiert auf einer vierstundigen Vorlesung mit dem Titel "Grundlagen der Theoretischen Informatik." Die Autoren fuhren an exemplarischen Problemstellungen der Theoretischen Informatik deren Losungen mit Rechnern von der Analyse des Problems bis zu seiner Implementation in einer prozeduralen Programmiersprache mit syntaktischer und semantischer Analyse vor, auch unter dem Aspekt der Verbindung von theoretischer Strenge und Praxisrelevanz. Mit Aufgaben und Losungshinweisen bzw. Losungen."

The human brain possesses the remarkable capability of understanding, - terpreting, and producing human language, thereby relying mostly on the left hemisphere. The ability to acquire language is innate as can be seen from d- orders such as speci?c language impairment (SLI), which manifests itself in a missing sense for grammaticality. Language exhibits strong compositionality and structure. Hence biological neural networks are naturally connected to processing and generation of high-level symbolic structures. Unlike their biological counterparts, arti?cial neural networks and logic do not...