Before revision:  We find a family of neural network models in which memory is acquired by means of biologically-inspired learning rules; the properties of these rules, in turn, determine the storing component in which memory can persist indefinitely. Memory representations manifest as time-varying attractors in neural state-space and support associative retrieval of learned information.
After revision:  We find a simple and general principle, stemming from stability arguments, that links eigenvalues in the complex plane to memories. Specifically, imaginary-coded memories are more resilient to noise and homeostatic plasticity than their real-coded counterparts. Memory representations are stored as time-varying attractors in neural state-space and support associative retrieval of learned information.