Higher cognitive capacities rely on the possibility to memorize, in the brain, noisy variables. Memories are generally understood to be realized as configurations of activity towards which specific populations of neurons are “attracted”, i.e towards which they dynamically converge, if properly cued. In the seminar, I will briefly show that biologically plausible self-organized learning rules can, counterintuitively, outperform optimized iterative algorithms in the ability to store discrete attractors. Then, I will mainly focus on the storage of the activity patterns of spatially selective cells, as place cells, neuronal candidates involved in the creation of cognitive maps. Recent experimental results showed that the activity patterns of place cells are highly irregular in complex environments, failing to be described by standard continuous attractors, which require homogeneity across units. Here we show that a continuous attractor theory can contemplate irregularities if relaxing the requirement of a continuous manifold of fixed points to a continuous dynamical flow, which, we see, persists up to a phase transition. This result leads us to hypothesize that place maps may be effectively memorized in continuous quasi-attractive manifolds.
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