Attractor properties of dynamical systems: neural network models

Abstract

We propose tools to probe the nature of attractors in dynamical systems. These include the activity distribution, the evolutions of the state damage, activity damage and temporal correlation damage. When they are used to study the retrieval attractors in dilute asymmetric neural networks, a transition from a partially frozen phase to an unfrozen phase is found for networks trained with sufficiently noisy data near storage saturation, and this confirms that the retrieval attractors are more chaotic in this case. We are also able to demonstrate that the retrieval attractors in dilute asymmetric neural networks are not clouds of attractors, but consist of a single chaotic attractor for each stored pattern. Furthermore, they facilitate the device of effective freezing procedures, which significantly improve the quality of retrieval in neural networks.