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#006B Vectorization and Broadcasting in Python

What is Vectorization? A vectorization is basically the art of getting rid of explicit for loops whenever possible. With the help of vectorization, operations are applied to whole arrays instead of individual elements. The rule of thumb to remember is to avoid using explicit loops in your code. Deep learning algorithms tend to shine when trained on large datasets, so it’s important that your code runs quickly. Otherwise, your code might take a long time…

#012A Building a Deep Neural Network

Building blocks of a Deep Neural Network In this post we will see what are the building blocks of a Deep Neural Network. We will pick one layer, for example layer $$l$$ of a deep neural network and we will focus on computatons for that layer. For layer $$l$$ we have parameters $$\textbf{W}^{[l]}$$ and . Calculation of the forward pass for layer we get as we input activations from the previous layer…

#010A Gradient Descent for Neural Networks

In this post we will see how to implement gradient descent for one hidden layer Neural Network as presented in the picture below. One hidden layer Neural Network   Parameters for one hidden layer Neural Network are $$\textbf{W}^{[1]}$$, $$b^{[1]}$$, $$\textbf{W}^{[2]}$$ and $$b^{[2]}$$. Number of unitis in each layer are:  input of a Neural Network is feature vector ,so the length of “zero” layer $$a^{[0]}$$ is the size of an input feature…
Activation functions When we build a neural network, one of the choices we have to make is what activation functions to use in the hidden layers as well as at the output unit of the  Neural Network. So far, we’ve just been using the sigmoid activation function but sometimes other choices can work much better.  Let’s take a look at some of the  options. $$sigmoid$$ activation function In the forward propagation steps for Neural Network there are two steps…
Vectorizing Across Multiple Training Examples In this post we will see how to vectorize across multiple training examples. The outcome will be similar to what we saw in Logistic Regression. Equations we defined in previous post are these: $$z^{[1]} =\textbf{W}^{[1]} x + b ^{[1]}$$ $$a^{[1]} = \sigma ( z^{[1]} )$$ $$z^{[2]} = \textbf{W}^{[2]} a^{[1]} + b ^{[2]}$$ $$a^{[2]} = \sigma ( z^{[2]} )$$ These equations tell us how, when given an…