In the structure of a neural network, are the early or later layers more affected by vanishing gradients?

Question Analysis

The question is asking about the concept of "vanishing gradients," which is a common issue in training deep neural networks. Understanding which layers are more affected by this problem will demonstrate your knowledge of neural network architectures and training dynamics. The question tests your understanding of backpropagation and how gradient descent updates the weights in a deep network.

Answer

In a neural network, vanishing gradients affect the earlier layers more significantly. Here's why:

• Backpropagation Process: During backpropagation, the gradient of the loss function is calculated with respect to each weight by the chain rule. As this gradient is propagated backward through the network, it is multiplied by the derivatives of the activation functions used in each layer.

• Activation Functions: Common activation functions like the sigmoid and hyperbolic tangent (tanh) have derivatives that are less than 1. When these derivatives are multiplied together over many layers, they can shrink exponentially, causing the gradients to become very small or "vanish."

• Impact on Early Layers: As a result, the earlier layers (those closer to the input) receive very small gradient updates, which means they learn very slowly compared to the later layers. This can hinder the network's ability to learn complex patterns in the data.

In summary, the early layers in a neural network are more affected by vanishing gradients because the gradient diminishes as it is propagated backward through the network.