Practical Aspects of Deep Learning - 2

Welcome to the second part of “Practical Aspects of Deep Learning”. If you haven’t already gone through the first part, then you can read the post here. In this post, we will be discussing on how to prevent the model from diverging from a good solution and also efficient processes to check the gradients of the network.

9. Normalizing Inputs

  • Before training a neural network, it is essential to normalize your input training set
  • It make the elongation between the feature axes of the dataset uniform, resulting in zero mean and unit standard deviation

  • Why do we need normalization?
    • It shrinks the cost function of the network as shown in the image below
    • This helps the model to learn faster even at a low learning rate
    • It also helps in easy and faster optimization

10. Vanishing and Exploding Gradients

  • For very deep neural networks, the activations can exponentially rise or diminish resulting in either exploding or vanishing gradients when backpropagating through the layers
  • The vanishing gradient problem decays information as it goes deep into the network, making the network to never converge on a good solution
    • Neurons in the earlier layers learn more slowly than the ones in the latter layers
  • The exploding gradient problem on the other hand makes the gradient bigger and bigger, and as a result forces the network to diverge
    • In this case, the earlier layers explode with very large gradients, making the model useless

11. Weight Initialization for Deep Neural Networks

  • Initializing weights W to zero
    • We know that if we initialize all the weights to zero, our network acts like a linear model as all the layers basically learn the same thing. This makes the model just a linear combination of layers
    • So, the most important thing is to not initialize all the weights to zero and use a random initialization approach
  • Initializing weights randomly
    • Although this may sound an appropriate approach to initialize the weights of a network, in some conditions (when proper activations are not used), it may lead to vanishing or exploding gradients
    • So, this method cannot be considered bullet proof although it works most of the time with RELU activations
  • Using some heuristic to initialize weights
    • This is considered as the proper way when it comes to weight initialization of deep neural networks
    • We can use some heuristics from the model to assign the weights of the layers according to the activation function used in a layer
    • The images below show how we should actually initialize weights in case of RELU, tanh, and other activations

  • NOTE: Here, “size_l” refers to the number of nodes in the lth layer, i.e. n[l]

  • This concludes the key points that you should be aware of when building a practical deep neural network. The image below demonstrates the workflow of a deep neural network along with forward and backward propagation. This might generate an intuition for you to build practical neural networks from scratch in Python.

  • It is very important to understand how forward propagation and backward propagation (with gradient descent) work in a deep neural network. The following formulae will always keep you in track when building a neural network from scratch.

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