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I am learning about neural networks and have a couple of things I don't understand.

Firstly, in competitive learning I understand that only the neuron with the strongest output is reinforced. That is done in a manners imilar to:

Δwi*j = I(j)*h(i)

Where w* indicates the 'winning' neuron, j indicates the input we are considering, I(j) is the value of such input and h(i) is the sum of all weighted inputs. This is repeated for each connection leading to the winning neuron.

My question is... Why? Why not simply, for example, increase the connection by an arbitrary amount? Or by another function? I have done quite some research, but still can't make sense of this.

Thanks!

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    $\begingroup$ I don't understand the formula. This site supports Latex, could you make it clearer? I don't know if you mean $\Delta w_i^* j$ or $\Delta w_{ij}^*$ or maybe $\Delta w i^* j$. Especially because in the next line you use $w^*$. And what's $i$? $\endgroup$ – Wandering Logic Mar 8 '15 at 21:13
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You actually can increase it by an arbitrary amount. The reason you are increasing it by the sum of all weighted inputs is so that the number you increment by is actually related to the neural network and the input. At least in that case, what you are incrementing by something that is related to what's going on. Otherwise, the behavior may be more random.

There are several functions you could choose to increment by instead. You could also choose to create new neurons (mitosis) where a neuron exceeds an arbitrary threshold. The method you're following is just another method that is being tested in trying to properly represent neural networks.

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