Continuous quasi-attractors dissolve with too much – or too little – variability

Hippocampal place cells in bats flying in a 200m tunnel have been shown to be active at multiple locations, with considerable variability in place field size and peak rate. We ask whether such disorderly representation of one’s own position in a large environment could be stored in memory through Hebbian plasticity, and be later retrieved from a partial cue. Simulating an autoassociative network in which similarly variable place fields are encoded with a covariance rule, we find that it may serve spatial memory only within a certain variability range, in particular of field width. The working range is flanked by two dysfunctional regions, accessed through apparent phase transitions. For a large network, phase boundaries can be estimated analytically to depend only on the number of fields per cell in one case, and to be a pure number in the other, implying a maximal size of the environment that can be stored in memory.