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While trying to understand artificial neural networks, I came upon an equation for finding the net input of an artificial neuron. Can someone explain this to me and what it means? Here is the original article

$$y_i=f\left(\sum_j w_{ij}y_j\right)$$

Thanks in advance, ell.

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Are you talking about the "weighted sum" formula? – Arturo Magidin Jan 31 '11 at 20:28
Are you referring to $$y_i=f\left(\sum_j w_{ij}y_j\right)$$ – Isaac Jan 31 '11 at 20:30
Yes :) Is there any way I can put that on my post with my current reputation? – Ell Jan 31 '11 at 20:39
@ell By writing MathJax markup. – Simon Kuang Jun 2 '14 at 2:46
up vote 4 down vote accepted

So hopefully you understand what the $\sum$ symbol means, it's just a summation across all of those indices. In this case we have our weight vectors


and our vector $y$. The neuron then is going to compute the new value of $y_i$, based on a dot product of $w_i$ with $y$. Hence

$\sum_{j} w_{ij}y_j$

is just dot product of $w_i$ and $y$, where both are $n$-dimensional vectors.

Then $f$ is an activation function, it could be a preceptron or it could be a linear node. So it may output the value of the net, or it may output a 0 or a 1 based on the value of the summation. Or it could have some non-linear neuron it all depends on the network.

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Thanks this helped a lot :) – Ell Jan 31 '11 at 21:12

What you are looking at is a simplistic model of the neuron. In particular, the inputs are dendrites and the outputs are the synapse.

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