(S)RAAM: An Analytical Technique for Fast and Reliable Derivation of Connectionist Symbol Structure Representations

Abstract

Recursive auto-associative memory (RAAM) has become established in the connectionist literature as a key contribution in the strive to develop connectionist representations of symbol structures. However, RAAMs use the backpropagation algorithm and therefore can be difficult to train and slow to learn. In addition, it is often hard to analyze exactly what a network has learnt and, therefore, it is difficult to state what composition mechanism is used by a RAAM for constructing representations. In this paper, we present an analytical version of RAAM, denoted as simplified RAAM or (S)RAAM. (S)RAAM models a RAAM very closely in that a single constructor matrix is derived which can be applied recursively to construct connectionist representations of symbol structures. The derivation, like RAAM, exhibits a moving target effect because training patterns adjust during learning but, unlike RAAM, the training is very fast. The analytical model allows a clear statement to be made about generalization characteristics and it can be shown that, in practice, the model will converge.

Keywords:

• (S)RAAM
• Raam
• Symbol Representation
• Principal Component Analysis
• Recurrent Networks
• Artificial Intelligence