The Reusable Symbol Problem

Examining the major differences between how traditional programs compute and our current understanding of how brains compute, I see only one key gap in our ability to carry out logical reasoning within neural networks using standard methods. I refer to this gap as the reusable symbol problem: How can neural systems use multiply-instantiatable symbols to represent arbitrary objects? This problem is fundamental and cannot be readily decomposed into simpler problems. Solving this problem would solve many individual problems such as the problem of representing relations between objects represented as neural activation patterns, the problem of implementing grammars in neural networks, and the well-known binding problem [3] for neural models. In this paper I discuss the use of reusable symbols and I give a concrete simple canonical example of the reusable symbol problem.