The vanishing and exploding gradient problems are significant challenges encountered when training deep neural networks.

The vanishing gradient problem occurs when gradients become very small as they are propagated back through the layers of the network. This often happens with activation functions like sigmoid or tanh, where the derivatives are less than one. As a result, the weights of the earlier layers receive minimal updates, leading to slow or halted learning. This issue is particularly pronounced in deep networks with many layers, making it difficult for the model to learn effectively ²³⁴.

Conversely, the exploding gradient problem arises when gradients become excessively large, causing drastic updates to the weights. This can lead to instability in the training process, where the model’s weights oscillate wildly or diverge entirely. This problem is often seen in recurrent neural networks (RNNs) and can result in the model failing to converge ³⁴.

To mitigate these issues, techniques such as using different activation functions (like ReLU), implementing LSTM networks, or employing gradient clipping can be effective ³⁴.