# Perceptron learning rule past exam question

I'm struggling to solve this past paper question and my lecturer is being less than helpful. The question is:

Apply the perceptron learning rule to update the current weight vector (0.1, 0.3) when the learning rate is 0.01, the input vector is (2.0, 4.0), and the error vector is (1, -1).

What has me confused is the use of vectors for the current weight, input and error value. We've never used vectors for this before (only regular numbers) and no examples I can find online use 2D vectors like this.

I know the perceptron learning rule is:

New weight = old weight + (learning rate * perceptron input * error value)


But I'm not sure how to do this kind of maths with 2D vectors to get a 2D vector as my result (which is what I assume I want, since the question seems to be asking for the new weight).

Firstly let me say that I am not going to solve this for you. What I would do instead is help you figure out how to solve it all by yourself.

• How many inputs will your perceptron have if your input vector is in n-D?
• Conceptually, what does the output from a perceptron represent?
• Following from the second point, what does updating the weights do to the output from your perceptron?
• Ideally, what should the updating of the weights do to the output?
• When do you need to update the weights?