Question

I’m trying to determine for the articial neuron shown below the values (0 or 1)
for the inputs i1, i2, and i3 for which it will fire (i0 is the input for the
bias weight and will always be -1).

The weights are

W0 = 1.5

W1 = -1

W2 = 1, and W3 = 2.

Assume the activation function depicted in image below.

Please clarify your answer as I have done few examples and still I’m not able to fully understand the theory 🙁

Many thanks,

Mary J.

PS. Image below:

Answer 1

You basically have the following equation for the neuron output, where i1, i2, and i3 can each have the value 0 or 1:

2*i3 + i2 - i1 - 1.5 >= 0

First, let’s look at the highest positively-weighted value. If i3 is 0, the most you can get for the left side is -0.5, so i3 has to be 1 to get a non-zero output. The equation then becomes:

i2 - i1 + 0.5 >= 0

Now look at the negatively-weighted value. If i1 is 0, the output will always be greater than zero no matter what i2 is. If i1 is 1, i2 has to be 1 as well for there to be a non-zero output.

You therefore have these combinations which create a non-zero output:

i1    i2    i3

0     0     1
0     1     1
1     1     1