A few last words about the neural network implementation

You may be wondering why we went through all of this theory just to implement a simple multilayer artificial network that can classify handwritten digits instead of using an open source Python machine learning library. In fact, we will introduce more complex neural network models in the next chapters, which we will train using the open source TensorFlow library (https://www.tensorflow.org). Although the from scratch implementation in this chapter seems a bit tedious at first, it was a good exercise for understanding the basics behind backpropagation and neural network training, and a basic understanding of algorithms is crucial for applying machine learning techniques appropriately and successfully.

Now that you have learned how feedforward neural networks work, we are ready to explore more sophisticated deep neural networks, such as TensorFlow and Keras (https://keras.io), which allow us to construct neural networks more efficiently...