Having established the basic structure and implementation of Recurrent Neural Networks, we now address the practical difficulties encountered during their training. RNNs, particularly when processing long sequences, can exhibit numerical instabilities within the backpropagation through time algorithm.

This chapter examines two primary challenges: the vanishing gradient problem, where error signals diminish exponentially as they propagate back through time (gradients approach $0$), and the exploding gradient problem, where these signals grow excessively large (gradients become numerically unstable). Both issues significantly impair the network's ability to learn dependencies across distant time steps, a primary reason for using RNNs.

You will learn why these gradient problems arise and explore standard techniques to mitigate them. We will cover gradient clipping to manage exploding gradients, discuss effective weight initialization strategies, and consider the impact of different activation functions within recurrent layers. Understanding these training dynamics is essential for building and tuning effective sequence models.