Perceiving spirals and inside/outside relations by a neural oscillator network

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 generic perspective that does not involve learning. We point out that the spiral problem is intrinsically connected to the inside/outside problem. We propose a solution to both problems based on oscillatory correlation using a time delay network. Our simulation results match human performance, and we interpret human limitations in terms of synchrony and time delays, both biologically plausible. As a special case, our network without time delays can always distinguish these figures regardless of shape, position, size, and orientation. We conjecture that visual perception will be effortful if local activation cannot be rapidly propagated, as synchrony would not be established in the presence of time delays.