Autoassociative memory is the capacity of recalling the full representation of a previously stored item, starting from a partial or noisy cue. Memory recall has been typically linked with patterns of persistent and graded neural activity, with rates far below saturation of the single-neuron I/O function (i.e. far below ~100 Hz). Attractor dynamics account naturally for the iterative retrieval of cued states, and are also thought to underlie the emergence of persistent activity in cortical circuits. However, models of attractor dynamics have fallen short of incorporating some key physiological constraints of cortical circuits in a unified way. Specifically, some models violate Dale's law (i.e. the same neuron may simultaneously excite and inhibit different postynaptic partners), while some others restrict the representation of memories to a binary format, or rely on the saturation of single-neuron activity at high rates.

Here we optimised the stability of a large number of graded activity patterns, using novel theoretical tools from robust control, by directly tuning the connectivity of a neural network under physiological constraints [1]. In particular, we enforced the segregation of excitatory (E) and inhibitory (I) neurons, and we modelled the single-neuron I/O function as an expansive function that did not saturate over a realistic dynamic range (0-100 Hz). We divided the network into principal and auxiliary populations (each potentially including both E and I cells), where the former were constrained to encode the desired memories and the latter were left free to adapt their activities during optimisation. We found that tuned excitatory connectivity, combined with precise inhibitory feedback, led to stable dynamics around a large number of fixed points. These attractor states could be recalled from noisy cues, and recall was also robust to ongoing noise in the dynamics. Moreover, the resulting networks displayed properties qualitatively comparable to biological circuits: they operated in the balanced regime, and both weight distributions and the pairwise statistic of synaptic connections matched experimental measurements. Our results also indicated qualitative differences between principal and auxiliary neurons in both the connectivity patterns they expressed and the sensitivity of the whole network to their perturbations. This offers novel experimentally testable predictions for establishing the functional role that different cortical neural subclasses play in memory recall.