so here there was a question that instead of initializing weight vector as zeroes what if we initialize to [1000 , -1000] (there is no offset i.e classifiers passing through origin). will the mistakes that the perceptron algorithm makes increases or decreases as it gets converged? Answer : It would significantly increase the number of mistakes.
Intuition that I have: the learning rate parameter affects only the scale of the weight vector, not the direction. so even if we take thetha = [1000, -1000] we cannot determine whether it makes less mistakes than [0,0] or not.