Gentner and Markman (1992) suggested that the ability to deal with analogy will be a "Watershed or Waterloo" for connectionist models. They identified "structural alignment" as the central aspect of analogy making. They noted the apparent ease with which people can perform structural alignment in a wide variety of tasks and were pessimistic about the prospects for the development of a distributed connectionist model that could be useful in performing structural alignment. In this paper I describe how Holographic Reduced Representations (HRRs) (Plate, 1991; Plate, 1994), a fixed-width distributed representation for nested structures, can be used to obtain fast estimates of analogical similarity.

Gentner and Markman (1992) suggested that the ability to deal with analogy will be a "Watershed or Waterloo" for connectionist models. They identified "structural alignment" as the central aspect of analogy making. They noted the apparent ease with which people can perform structural alignment in a wide variety of tasks and were pessimistic about the of a distributed connectionist model that could be useful inprospects for the development performing structural alignment. In this paper I describe how Holographic Reduced Representations (HRRs) (Plate, 1991; Plate, 1994), a fixed-width distributed representation for nested structures, can be used to obtain fast estimates of analogical similarity.

Holographic Recurrent Networks (HRNs) are recurrent networks which incorporate associative memory techniques for storing sequential structure. HRNs can be easily and quickly trained using gradient descent techniques to generate sequences of discrete outputs and trajectories through continuous spaee. The performance of HRNs is found to be superior to that of ordinary recurrent networks on these sequence generation tasks.

Holographic Recurrent Networks (HRNs) are recurrent networks which incorporate associative memory techniques for storing sequential structure.HRNs can be easily and quickly trained using gradient descent techniques to generate sequences of discrete outputs andtrajectories through continuous spaee. The performance of HRNs is found to be superior to that of ordinary recurrent networks onthese sequence generation tasks. 1 INTRODUCTION The representation and processing of data with complex structure in neural networks remains a challenge. In a previous paper [Plate, 1991b] I described Holographic Reduced Representations(HRRs) which use circular-convolution associative-memory to embody sequential and recursive structure in fixed-width distributed representations. Thispaper introduces Holographic Recurrent Networks (HRNs), which are recurrent nets that incorporate these techniques for generating sequences of symbols or trajectories through continuous space.