# Decision boundary of an neural network Starting with a).

For the first unit: 0 * x1 + 1 * x2 + 1 > 0 (0, because the threshold is 0) which is the same as x2+1 > 0.

For the second unit: x1 * 1 + x2 * 0 + 1 > 0 (0, because the threshold is 0) which is the same as x1 + 1 > 0.

For the third unit: x1 * 1 + x2 * 1 + 1 > -1 (-1, because the threshold is -1. I might have misunderstood this since the assignment states "Circles indicate threshold units with threshold at zero...") which is the same as x1 + x2 > -2.

I then draw those lines. Is it correct so far? I can't however figure out how to solve b) How do I take the bias on the output node into account?

This is the given solution (but I don't understand how they got it): Thanks!!

• I think you mixed intercept and threshold. The threshold is set to zero (read the text). The intercept is 1 * 0.0 for the first two nodes and 1 * (-1.0) for third one. This leads to different inequalities. Mar 10 at 13:05
• By the way: this looks like you are asking to do your homework. I know such kind of networks mainly from text books and for educational purposes. Mar 10 at 13:07
• Thanks for your reply! I thought I was supposed to use this equation Σwjxj+bias=threshold for the nodes. But I guess that isn't the case since I get the wrong answer if I just plugg in bias = 1 and threshold = 0, and I don't see anything about any 'intercept'. What equation should I use? I feel a bit lost and I'm having a hard time figuring out how it all fits together. @Broele Mar 10 at 13:27
• Bias and intercept mean the same, here Mar 10 at 13:50
• Ok thanks! But what do the numbers next to the filled in circles stand for? I thought those were the bias. @Broele Mar 10 at 14:01