# Choosing perceptron weights to achieve 0% error

I'm really not sure what to do for this question, although I think I would be able to do q3 if I knew how to do q2

• What have you tried? Your question does not specify what activation function is being used. If the activation function is ReLU, then you just need to pick real numbers $w_0, w_1, w_2$ such that $x_1 \,\operatorname{AND} \, x_2 = \max\{0, w_0 + w_1 x_1 + w_2 x_2\}$ for all $x_1,x_2 \in \{0, 1\}$. This can be done by inspection/trial and error – Artem Mavrin Apr 4 '19 at 20:45
• @ArtemMavrin, I managed to figure it out for the AND function by picking w0=-1, and w1=w2=1, but I'm not sure how to do it for the OR function – user243609 Apr 4 '19 at 21:16
• Is there another affine transformation after the activation? The actual perceptron structure isn't included in the question. If you are allowed to perform an affine transformation after the activation, then you can use the fact that $x_1 \,\operatorname{OR}\, x_2 = 1 - ((1 - x_1) \, \operatorname{AND} \, (1-x_2))$ together with your solution for the AND problem – Artem Mavrin Apr 4 '19 at 21:19