    Gain insights into building and optimizing neural networks in Python. Delve into fundamental concepts, mathematical explanations, and practical implementations to enhance your machine learning skills.

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Machine learning is one of the fastest growing fields, and we cannot emphasize enough about its importance. This course aims to teach one of the fundamental concepts of machine learning, i.e., Neural Network. You will learn the basic concepts of building a model as well as the mathematical explanation behind Neural Network and based on that; you will build one from scratch (in Python). You will also learn how to train and optimize your network to achieve a better result.

Make Your Own Neural Network in Python

# Structure of the neural network 
One thing we haven't yet tried, and perhaps we should have earlier, is to change the shape of the neural network. Let's try changing the number of middle hidden layer nodes. We've had them set to $100$ for far too long! 

Before we jump in and run experiments with different numbers of hidden nodes, let's think about what might happen. The hidden layer is the layer where the learning happens. Remember, the input nodes simply bring in the input signals, and the output nodes simply push out the network's answer. It's the hidden layer (or layers), that has to turn the input into the answer. It's where the learning happens. Actually, it's the link weights before and after the hidden nodes that do the learning.

If we had too few hidden nodes, say three, we can imagine there is not enough space to learn whatever a network learns, and to somehow turn all the inputs into the correct outputs. It would be like asking a car with five seats to carry ten people. We just can't fit that much stuff inside. Computer scientists call this kind of limit a **learning capacity**. We can't learn more than the learning capacity, but we can change the vehicle, or the network shape, to increase the capacity.

What if we had 10,000 hidden nodes? Well, we won't be short of learning capacity, but we might find it harder to train the network because now there are too many options for where the learning should go. Maybe it would take 10,000 epochs to train such a network. 

# The effect of hidden layers on performance 
Let's run some experiments and see what happens.

Explore the effect of the number of hidden layers on the accuracy of results.

Prologue

A Little Background

Let's Get Started!

Backward Propagation of Error

Adjusting the Link Weights

A Gentle Start with Python

Neural Network with Python

Testing Neural Network against MNIST Dataset

Some Suggested Improvements

Even More Fun!

Epilogue

Appendix: A Small Guide to Calculus

Change the Network Shape

Structure of the neural network