Recurrent networks for structured data - A unifying approach and its properties

We consider recurrent neural networks which deal with symbolic formulas, terms, or, generally speaking, tree-structured data. Approaches like the recursive autoassociative memory, discrete-time recurrent networks, folding networks, tensor construction, holographic reduced representations, and recursive reduced descriptions fall into this category. They share the basic dynamics of how structured data are processed: the approaches recursively encode symbolic data into a connectionistic representation or decode symbolic data from a connectionistic representation by means of a simple neural function. In this paper, we give an overview of the ability of neural networks with these dynamics to encode and decode tree-structured symbolic data. The correlated tasks, approximating and learning mappings where the input domain or the output domain may consist of structured symbolic data, are examined as well.