Perceiving geometric patterns: from spirals to inside-outside relations

Since first proposed by Minsky and Papert (1969), the spiral problem is well known in neural networks. It receives much attention as a benchmark for various learning algorithms. Unlike previous work that emphasizes learning, we approach the problem from a different perspective. We point out that the spiral problem is intrinsically connected to the inside-outside problem proposed by Ullman (1984, 1996). We propose a solution to both problems based on oscillatory correlation using a time-delay network. Our simulation results are qualitatively consistent with human performance, and we interpret human limitations in terms of synchrony and time delays. As a special case, our network without time delays can always distinguish these figures regardless of shape, position, size, and orientation.