Unraveling the Mystery of Feature Learning in Deep Neural Networks

In this paper, we explore the relationship between the learning rate and depth in neural networks (NNs). Specifically, we examine how the size of the learning rate, represented by η0, affects the change in the network’s loss function, L. We find that as the depth of the network increases, the influence of the learning rate on the loss function also increases, making it essential to have a suitable value for η0.
To better understand this relationship, let’s consider an analogy. Imagine you are trying to build a tower out of blocks. Each block represents a neuron in the network, and the way you stack them determines the connections between them. Just like how you need to adjust the size of each block to make the tower stable, we need to adjust the learning rate to make sure the network learns effectively.
We also find that the loss function, L, is related to the output of the network. In other words, how well the network performs at classifying objects or solving problems. As the depth of the network increases, the number of layers that contribute to the output also increases, making it more challenging to accurately predict the loss.
To address this challenge, we propose a novel approach to adjusting the learning rate based on the depth of the network. By using a suitable value for η0, we can ensure that the network learns effectively and efficiently, even as the depth increases. This approach allows us to achieve better performance in NNs while maintaining a manageable number of degrees of freedom.
In summary, our paper sheds light on the complex relationship between the learning rate and depth in NNs, providing valuable insights for practitioners and researchers alike. By using everyday language and engaging analogies, we demystify complex concepts and show how to adjust the learning rate for optimal performance.