There is an example related to perceptron learning, but I couldn't get it, I don't exactly know how to solve it.
There is a snippet from lecture notes.
What is the transformation between epochs?
There is no transformation between epochs. One full iteration over the training set is considered an epoch.
You train your perceptron on a data set. During one iteration over this entire training set, you:
Transformation of weights happens during epochs, not between epochs.
Ergo, weights may be changed for each data point in the training set. Oftentimes you would need to iterate over the entire set several times, before the weights converge (stabilize / stop changing).
What use is the number of epochs?
The number of iterations is significant as a measure of efficiency of the current algorithm under the current learning rate, for the current dataset. In short: You could use it for comparisons between learning rates, training sets or algorithms.