This is Appendix A to the thesis " Learning to See Analogies: a Connectionist Exploration."

this reportedly improved the learning. And still another important contribution in this work was a method for representing recursive structures -- by means of symbolic transformation of any tree structure into a binary tree, which can easily be transformed to a sequence. Those two operations are reversible,

A very natural approach to categorization is similaritybased clustering. We propose a visual representation which can be used with such a mechanism for the acquisition of spatial relation categories. We also show how supervision can be helpful in cases where basic similarity is low by proposing a learning mechanism which operates both in the presence and in the absence of words. Motivation Words signifying spatial relationships between objects are quite common in human languages. Such words, like the English ABOVE, cannot be adequately explained in terms of other words (Harnad, 1990). The core of their meaning is rather directly associated with visual perception. This means that to a significant extent, the acquisition of spatial relation concepts has to be independent of language (Choi and Bowerman, 1991, Regier, 1992). This, in turn, implies that humans have some innate capability to automatically form spatial relation concepts, by noticing regularities in their visual inpu...