    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

# How a neural network works
A network with three layers of neurons, with each neuron connected to every other in the previous and next layer, looks pretty amazing. But the idea of calculating how signals progress from the inputs through the layers to become the outputs may seem a little daunting.

We agree that it is hard work, but it is also important to illustrate how a neural network works so we always know what is really happening inside it, even if we later use a computer to do all the work for us. So, let's try looking at a smaller neural network with only two layers, each with two neurons. This is shown in the illustration below.


Let’s imagine the two inputs are $1.0$ and $0.5$. The following illustration shows these inputs entering this smaller neural network.

Just like before, each node turns the sum of the inputs into an output using an activation function. We will also use the sigmoid function

$$
y = \frac{1}{1 + e^{-x}}
$$
that we saw before, where $x$ is the sum of incoming signals to a neuron and $y$ is the output of that neuron. But what about the weights? That's a very good question. What value should they start with? Let's start with some random weights:

- $w_{1,1} = 0.9$

- $w_{1,2} = 0.2$

- $w_{2,1} = 0.3$

- $w_{2,2} = 0.8$

Random starting values aren't a bad idea, and it is what we did when we chose an initial slope value for the simple linear classifiers we looked at earlier. We improved our random values  with each example that the classifier learned from. The same should be true for neural network link weights.

There are only four weights in this small neural network, as that's the total number of combinations for connecting the two nodes in each layer. The following diagram shows all these numbers marked.

Understand how a smaller neural network works with only two layers, each with two neurons.

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

Follow Signals through a Simple Network

How a neural network works