Fig. 7: Modeling of single-field emergence via competitive learning.

a Model architecture. A total of 3000 GCs receive excitatory inputs from 300 LV cells and 300 grid cells from the EC and are subjected to feedback inhibition. The EC-to-GC synaptic weight matrix is referred to as Wij. The threshold used as feedback inhibition is referred to as I. Color coded, rate maps of EC LV cells (upper) and grid cells (lower). The firing fields were generated with Gaussian functions. LV cells encode various distances to landmarks, while grid cells have various spatial phases and the same periodicity as periodic cells. In red, the effect of MC feedforward inhibition is added to the model. The spatial modulation of MC activity is assumed to be proportional to the dynamic range of EC average activity. The color scale is the same as that used in (c). b All operations executed during one model iteration. (1) The excitation Ej received by the GCj in a given position. (2) The firing rate of GCj and (3) the feedback inhibition I in that position. The value of I is estimated numerically by finding the value among a range of I values that best satisfies relations (2) and (3). (4) The potentiation of synaptic weights, proportional to the level of cells’ co-firing throughout the belt. (5) The normalization of synaptic weights. c Transformation of spatial representations across iterations. Color-coded representation of rate maps for active GCs, across iterations. Active cells have a mean activity >0 and are sorted according to firing field positions. Note the increase in the number of active GCs (lower left numbers) and the transformation of representations from multiple to single place fields. d Evolution of the fraction of single, LV and periodic fields across iterations. e For each active GC, the color-coded representation of the total synaptic weight contributed by grid cells and by each population of LV cells (encoding a specific landmark) is shown across iterations using the same GC ordering as in (c). Note that synaptic inputs initially originate from one source and are progressively redistributed equally among grid cells and LV cells. f Effect of the distinct magnitude of MC modulation on the GC mean activity.