    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

# The `query()` function 

Before we start working on the code that trains the neural network by fleshing out the currently empty `train()` function, we'll work on the simpler `query()` function. This will give us more time to build confidence and get some practice at using both Python and these weight matrices inside the neural network object. 

The `query()` function takes the input to a neural network and returns the network’s output. That’s simple enough, but to do that, we need to pass the input signals from the input layer of nodes, through the hidden layer and out of the final output layer. We'll also need to remember that we use the link weights to moderate the signals as they feed into any given hidden or output node. Moreover, we also use the sigmoid activation function to squish the signal coming out of those nodes. 

If we had lots of nodes, we'd have the time-intensive task of writing out the Python code for each of those nodes, doing the weight moderating, summing signals, and applying the activation function. And the more nodes we have, the more code we need.


# Simple implementation
Luckily, we don’t have to do that because we worked out how to write all these instructions in a simple, concise matrix form. The following equation shows how the matrix of weights for the link between the input and hidden layers can be combined with the matrix of inputs to give the signals into the hidden layer nodes:

$$

X_\text{hidden} = W_\text{input\_hidden} \cdot I

$$

Not only is it was easier for us to write down, but programming languages like Python can also understand matrices and do all the real work quite efficiently because they recognize the similarities between all the underlying calculations.

The following code applies the NumPy library’s dot product function for matrices to the link weights $W_\text{input\_hidden}$ and the inputs $I$: 


Learn about the query() function, which is used to train the neural network, and its simple matrix form implementation.

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

Query the Network

The `query()` function

Query the Network

The query() function

The `query()` function