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Copying and Evolution of Neuronal Topology

Figure 4

Part A

(top) Formation of a topographic map using Hebbian learning and lateral inhibition. Assume that layer 0 (green neurons) project to layer 1 (yellow neurons) via initially all-to-all Hebbian Oja type neurons (purple). Weights in L0 are fixed (in this case only the weight from A to B is strong, all others are weak), and weights in L1 are plastic due to STDP. (bottom) There is all-to-all lateral inhibition in L1. Part B. A fixed topology I/O map with vertical correspondences is used to calculate the functions mapped by L0 and L1. Part C. “Shifts” and “Compression” are observed when the Hebbian learning+Oja rule+lateral inhibition algorithm is used in stochastic simulation using Izhikevich neurons [53]. See that the thick blue weights connecting L0 to L1 in Part C are not perfectly vertical, and neither are they always injective. In Part C(1) we see a “shift”, i.e. the representation of neuron B is shifted to the A′ position. Part C(5) and Part C(6) also contain shifts. However, in Part C(2) there is a perfect vertical mapping. In Part C(3) there is a “compression”. Compressions occur when the two (or more) parental neurons are highly correlated. In such a case, copying with compression may in fact be functionally beneficial in reducing information redundancy. In further experiments we assume perfect vertical strong connections.

Figure 4