  What is the physiological basis of long-term memory? The prevailing view in
neuroscience attributes changes in synaptic efficacy to memory acquisition.
This view implies that stable memories correspond to stable connectivity
patterns. However, an increasing body of experimental evidence points to
significant, activity-independent dynamics in synaptic strengths. Motivated by
these observations, we explore the possibility of memory storage within a
global component of network connectivity, while individual connections
fluctuate. 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. Our results suggest a
link between the properties of learning rules and those of network-level memory
representations, and point at measurable signatures to be sought in
experimental data.
