Previously in the last article, I had described the Neural Network and had given you a practical approach for training your own Neural Network using a Framework (Keras), Today's article will be short as I will not be diving into the maths behind Neural but will be telling how we create our own Neural Network from Scratch .

#### We will be using the MNIST dataset. For just importing the dataset we will be using Keras and all other will be written using numpy.

### The backpropagation

The toughest part that you might face during the whole code will be How does this Backpropagation works and what is the logic behind this.

Let me explain something that is very simple and might be very easy to understand. Let’s say that you want to minimize some variable ‘y*’ *with respect to a variable ‘x*’ *so what we do is:

Yes you got it right we do differentiate it and apply the condition of *dy/dx=0*

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Now, this is similar to what happens in backpropagation too. We have a loss function after the end of feed-forward which needs to be minimized with respect to the weights vector or matrices of each layer. So basically what we have to do is find *dc/dw*(n)…..to *dc/dw*(1) and finally multiply it with the learning rate and finally subtract it from the corresponding ‘w’s after each set of the epoch.

So if this is so easy why shouldn't you first try on your own for a single layer and then finally see my code.

#### We will be covering three layers of Neural Network and will be constructing it from scratch.

### The FeedForward :

As I had explained earlier in my post of Neural Networks we have a linear line function whose output is given non-linearity with the help of activation function like ReLu, Sigmoid, Softmax,tanh and many more

Our feedforward equation is given by —

** y=wx+b **where y is the output and w are the weights and for now we neglect the bias values.

So if we have a three-layer neural network we have:

#Making of feed-forward function

import numpy as np

def sig(s):

return 1/(1+np.exp(-1*s))

def sig_der(s):

return s*(1-s)

class NN:

def __init__(self,x,y):

self.x = x

self.y = y

self.n = 64 #no of neurons in the middle layers

self.input_dim = 784

self.out_dim = 10

self.w1 = np.random.randn(784,self.n)

self.w2 = np.random.randn(self.n,self.n)

self.w3 = np.random.randn(self.n,10)

def feedforward(self):

self.z1 = np.dot(self.x,self.w1)

self.a1 = sig(self.z1)

self.z2 = np.dot(self.a1,self.w2)

self.a2 = sig(self.z2)

self.z3 = np.dot(self.a2,self.w3)

self.a3 = sig(self.z3)

Till now we have built our normal feedforward network which requires actually minimal thinking. Now, lets start off with the hard part *THE BACKPROPAGATION.*

### Code the Hard BACKPROP

Now basically what does neural network do is that it first passes on the random set values through the layers and predicts a value and compares it with the actual image and gets the error, now the task is to minimize this error and how we do it is by using the basic chain rule of derivatives.

dc/dw3 = dc/da3 * da3/dz3 * dz3/dw3

Basically, as we are doing a classification problem and thus we will be using cross_entropy for this.

def cross_entropy(real,pred):

return (pred - real)/number of samples

so dc/da3 * da3/dz3 = a3 - y

and dz3/dw3 = a2

dc/dw2 = dc/da3 * da3/dz3 * dz3/da2 * da2/dz2 * dz2/dw2

#The upper equation is simply followed by a simple chain rule

dc/w1 = dc/da3 * da3/dz3 * dz3/da2 * da2/dz2 * dz2/da2 * da2/dz1 * dz1/dw1

I will not be writing the code for backpropagation but I have provided enough information to write the code. Just write and can confirm it through

The only track you have to keep is the matrix size that is used if that is handled carefully your output will be perfect

dubesar/Mnist-Character-Prediction-Tenserflow-Deep-neural-Network

And finally, if you have more interests regarding neural networks you can try out the similar problem for Dogs vs Cats Dataset and see the accuracy. In the next article, I will be starting off with CNN — Convolutional Neural Networks.

We will also write Convolutional Neural Networks from Scratch and also through Keras.

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Neural Network from Scratch was originally published in Becoming Human: Artificial Intelligence Magazine on Medium, where people are continuing the conversation by highlighting and responding to this story.