What does $y_i=f(\sum_j w_{ij}y_j)$ mean (in an artificial neuron model)?

Question

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.

Answer 1

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

$w_1,w_2,\dots,w_n$

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.

Answer 2

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