This segment explains the vanishing gradient problem that arises when training deep neural networks with sigmoid activation functions. It details how repeated multiplication by the small derivative of the sigmoid function during backpropagation leads to increasingly smaller deltas, hindering the effective updating of weights in earlier layers and slowing down or preventing convergence. The visualization of the computational graph and mathematical expressions for loss and deltas clarifies the chain rule's extensive application and the resulting challenges. This segment discusses solutions to the vanishing gradient problem. It explains how changing weight matrix initialization to larger values can counteract the diminishing deltas. The primary focus is on the shift from sigmoid to ReLU activation functions, highlighting ReLU's derivative of one for non-zero outputs, which significantly reduces gradient squishing. The segment also touches upon the potential for exploding gradients with ReLU and the importance of appropriate weight initialization strategies depending on the activation function used, emphasizing the role of modern deep learning libraries in handling this automatically. Deep neural networks with many layers face vanishing or exploding gradients during training. Sigmoid activations cause vanishing gradients due to their small derivatives, hindering weight updates in early layers. ReLU activations mitigate this but risk exploding gradients with large weights. Proper weight initialization and using ReLU (with careful weight scaling) are key to training deep networks effectively.