Which of the following statements are true about the learning rate in Neural Networks?

$1)$ Learning rate is defined as a factor that decides the amount by which the weights are updated.

$2)$ If the learning rate is set too low, then the weight changes may be so big that the optimization may overshoot the minima and increase the error.

$3)$ If the learning rate is set too high, training will progress very slowly as very tiny updates are made to the weights in the network.