# A Neural Net From Scratch

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This post is an example of regression, where we will use supervised learning (a model that returns a function after giving it an input and output). The goal is to find the temperature conversion equation. **The complete code is at the end of the article.**

First, we import NumPy, then defining the training set x_train and y_train. x_train is the independent variable representing temperature in Celsius, while y_train is the dependent variable representing the temperature in Fahrenheit.

x_train is divided by zero because large numbers are not stable; try to run the model without it for 100 epochs, and the loss function will return **inf**.

import numpy as npx_train = np.array([[-40.], [-30], [-20], [-10], [0], [10], [20], [30], [40]])/100y_train = np.array([31.28, 31.46, 31.64, 31.82, 32., 32.18, 32.36, 32.54, 32.72])

The code has five functions: forward, backward, loss, step, and model.

**Function 1: forward()**

The function returns the multiplication of the parameter weight with the dependent variable and adding the parameter bias.

`def forward(w, x, b): return np.float(w*x+b)`

**Function 2: backward()**

This function calculates the gradients; it guides the model in the right direction.

`def backward(x, y, pred, dw, db):`

dw = dw + (-2)*x*(y-pred)

db = db + (-2)*(y-pred)

return dw, db

Know how did we come up with this equation?

It’s the partial derivative of the loss function, more on calculus in this article:

**Function 3: loss()**

This example uses Mean Squared Error (MSE) as the loss function.

`def loss(y, pred): return np.array(np.square(y-pred).mean())`

**Function 4: step()**

The optimizer step uses the learning rate and gradients to update the parameters.

`def step(w, b, dw, db, lr=.01):`

w = w - lr * dw

b = b - lr * db

return w, b

**Function 5: model()**

The model calls all the functions above since we have a single neuron with two parameters, a weight, and a bias.

At the nested loop, we zero the gradients because every epoch is a fresh start. Then we call the forward and the backward function, followed by printing the loss and updating the parameters. **Code completed!**

def model(x, y, epoch=10):

m = x.shape[0]

w = 1.

b = 0 for i in range(epoch):

print(f'----------epoch: {i}-------') dw, db = 0, 0

for j in range(m):

pred = forward(w, x[j], b)

dw, db = backward(x[j], y[j], pred,dw, db) print(f'loss: {loss(y, pred)}') w, b = step(w,b,dw,db, lr=.1) return w, b

After running the code for 50 epochs, the loss function got minimized.

`>>> w, b = model(x_train, y_train, 50)`

----------epoch: 0-------

loss: 998.7760000000001

----------epoch: 1-------

loss: 678.2142745600001

----------epoch: 2-------

loss: 400.5283809648645

...

----------epoch: 47-------

loss: 0.7345516170916814

----------epoch: 48-------

loss: 0.7323773915041649

----------epoch: 49-------

loss: 0.7343447652825804

The result, w =~1.8 and b =~32, the constants we were after.

`>>> print(w[0], b)`

1.7986596334086586 31.999543280738333

Now to convert from Celsius to Fahrenheit, you can reuse the forward function as a calculator, for example:

`>>> forward(w, 100, b)`

211.8655066216042

Now, is the correct way to solve a linear function, no. But, It is a simple exercise for beginners. I hope that helps.