Why are the ANN training and validation accuracy graphs not smooth?
Considering that your validation accuracy has bigger steps than your training accuracy, this may simply be an issue of data size. Accuracy counts correct/not correct, so if the model switches its opinion on a sample the accuracy increases suddenly. Because your validation data is likely smaller than the training data the steps are bigger there.
There is nothing to worry about, this looks normal. On the other hand your validation loss is increasing, so you are overfitting.