Wandering mind: a self-trapping network can converge to attractors far from the initial state

The self-trapping attractor neural network (STN) is a naturally sparsely-connected dynamical attractor network that models short- and long-term associative memory. Long-term storage is modeled with sparse Hebbian synapses. Unlike homogeneous dynamical models of associative memory, the STN also includes back-projections from a coupled system that computes overlaps with stored memories. The coupled system sends one output for each stored memory to the sparsely-connected network, modeling hippocampal cortical pathways. Each output increases monotonically with the magnitude of the overlap of the system state with an individual stored memory, cooperating with Hebbian synaptic influences to produce ordered activity patterns that correspond to short-term storage. The research reported here tests the hypothesis that slow dynamics in the coupled system allow the sparsely-connected network to wander to the vicinity of attractors far from the initial state. Results confirm this hypothesis for the case of strong recurrent inputs and incomplete learning (weak synapses) in the attractor network