Recursive Networks: An Overview of Theoretical Results

A naturally structured information is typical in symbolic processing. Nonetheless, learning in connectionism is usually related to poorly organized data, like arrays or sequences. For these types of data, classical neural networks are proven to be universal approximators. Recently, recursive networks were introduced in order to deal with structured data. They also represent a universal tool to approximate mappings between graphs and real vector spaces. In this paper, an overview of the present state of the art on approximation in recursive networks is carried on. Finally, some results on generalization are reviewed, establishing the VC-dimension for recursive architectures of fixed size.