Adventures in Machine Learning

Mastering Backpropagation: Building Accurate Neural Networks in Python

Backpropagation Algorithm: Understanding the Importance and Working in Python

Artificial intelligence and machine learning have brought incredible advancements in technology. One of the most popular machine learning techniques is neural networks.

Neural networks are composed of several layers of neurons that are trained to recognize specific patterns in the data. The accuracy of the neural networks depends on the efficiency of the training process.

This is where a crucial algorithm, called backpropagation, comes into play. Backpropagation is a supervised learning algorithm that trains neural networks by adjusting their weights and biases until they can accurately predict the desired output.

It is a form of gradient descent, which means it iteratively minimizes the error between the expected output and the actual output.

But why is backpropagation algorithm so important?

The answer lies in the accuracy of neural networks. Neural networks are widely used in image and speech recognition, autonomous vehicles, and natural language processing, among other applications.

The accuracy of these applications depends on the accuracy of the neural networks, which, in turn, depends on the accuracy of the backpropagation algorithm.

Working of Backpropagation in Python

The backpropagation algorithm works by propagating the errors from the output layer back to the input layer. Neural networks have three layers: input layer, hidden layer, and output layer.

The input layer contains the data, the hidden layer processes the data, and the output layer produces the prediction. In a feed-forward neural network that uses the backpropagation algorithm, the data is passed through the input layer to the hidden layer, and then to the output layer.

The output layer produces a prediction, which is compared to the expected output. The difference between the predicted output and the expected output, known as the error, is then calculated.

The error is then propagated back through the layers, starting from the output layer to the hidden layer, and then to the input layer. The backpropagation algorithm adjusts the weights and biases of the neurons in each layer to minimize the error iteratively.

Lets take an example to understand the working of the backpropagation algorithm in Python. Suppose we want to train a neural network to recognize handwritten digits in an image.

We can use the MNIST dataset, which contains 60,000 training images and 10,000 test images of handwritten digits. First, we need to preprocess the data by converting the images to grayscale and resizing them to a standard size.

We then split the data into training and testing sets. Next, we define the structure of the network, including the number of neurons in each layer and the activation function of each neuron.

We then initialize the weights and biases randomly and start training the network using the backpropagation algorithm. During training, we feed the training data to the network and adjust the weights and biases to minimize the error.

We repeat this process for several epochs until the error is minimized. Once the network is trained, we test it on the test data to evaluate its accuracy.

We can also visualize the activations of the neurons in each layer to understand how the network makes its prediction.

Types of Backpropagation

There are two types of backpropagation: static backpropagation and recurrent backpropagation. Static Backpropagation:

In static backpropagation, the inputs and outputs are known beforehand, and the neural network is trained to produce the desired outputs for the given inputs.

This type of backpropagation is commonly used in applications like Optical Character Recognition (OCR), where the inputs and outputs are predetermined. The neural network is trained using a set of training data, and the weights and biases are adjusted to minimize the error between the predicted output and the expected output.

Recurrent Backpropagation:

In recurrent backpropagation, the inputs are not static, and the neural network needs to predict a sequence of outputs based on the inputs. The neural network operates in a feedback loop, where the output of the previous time step is used as input for the current time step.

This type of backpropagation is commonly used in applications like speech recognition, where the output depends on the previous outputs. In recurrent backpropagation, there are two types of values: definite values and threshold values.

Definite values are assigned to the inputs, and threshold values are assigned to the outputs. The error is propagated through the network iteratively until it converges to a minimum.


In conclusion, the backpropagation algorithm is a fundamental technique used in neural networks for supervised learning. It is essential for achieving high accuracy in applications such as image and speech recognition, autonomous vehicles, and natural language processing.

Understanding the working of the backpropagation algorithm in Python is crucial for developing efficient neural networks. By using types of backpropagation, such as static and recurrent, we can train neural networks to recognize patterns in data and make accurate predictions.

Implementation of Backpropagation in Python: A Step-By-Step Guide

Backpropagation algorithm is a popular technique for training artificial neural networks. When implemented correctly, it can help achieve high accuracy and efficiency in machine learning applications.

In this article, we will walk through the process of implementing backpropagation in Python and cover the necessary steps of importing libraries, loading the dataset, splitting the dataset into training and testing, initializing hyperparameters, creating helper functions, building the backpropagation model, and highlight the potential advantages and disadvantages of this algorithm. Importing Libraries:

In order to implement backpropagation in Python, we need to import the necessary libraries.

Numpy, Pandas, Scikit-learn, and Matplotlib are some commonly used libraries for machine learning. NumPy provides arrays that help in handling large amounts of data efficiently, pandas help in data manipulation, scikit-learn provides inbuilt functions to load and process datasets, and matplotlib helps to visualize the data.

The following lines of code import these libraries:

import numpy as np

import pandas as pd

from sklearn.datasets import load_iris

from sklearn.model_selection import train_test_split

import matplotlib.pyplot as plt

Loading the Dataset:

The iris dataset is a standard dataset that contains information about various flower species. The dataset contains 150 samples, each with four features (sepal length, sepal width, petal length, and petal width), and a target variable (species of flower).

We can load the dataset using the load_iris() function provided by scikit-learn, as shown below:

iris = load_iris()

X =

Y =

Splitting Dataset in Training and Testing:

We will split the dataset into training and testing sets, using the train_test_split() function provided by scikit-learn. The following code splits the data into 70% training and 30% testing sets:

x_train, x_test, y_train, y_test = train_test_split(X, Y, test_size=0.3)

Initializing Hyperparameters:

Before building the backpropagation model, we need to initialize some hyperparameters.

These hyperparameters include the learning rate, number of iterations, number of input nodes, number of hidden nodes, and number of output nodes. The following code initializes these hyperparameters:

learning_rate = 0.1

iterations = 1000

input_size = X.shape[1]

hidden_size = 4

output_size = len(np.unique(Y))

Creating Helper Functions:

We need to create several helper functions to build the backpropagation algorithm.

These functions include the sigmoid function that introduces non-linearity into our model, the mean squared error for calculating the difference between expected and actual outputs, and the accuracy function that measures how well the model performs. The following code defines these functions:

def sigmoid(x):

return 1/(1 + np.exp(-x))

def mean_squared_error(y_true, y_pred):

return np.mean((y_true – y_pred)**2)

def accuracy(y_true, y_pred):

return np.sum(y_true == y_pred)/len(y_true)

Building the Backpropagation Model:

We will build the backpropagation model using the following steps:


Initialize weights and biases randomly. 2.

For every iteration, compute the output by forward propagating the input through the network. 3.

Calculate the error between actual and expected outputs. 4.

Propagate the error backward to update the weights and biases. 5.

Repeat the process for a fixed number of iterations. The following code implements these steps:

W1 = np.random.rand(input_size,hidden_size)

b1 = np.random.rand(hidden_size)

W2 = np.random.rand(hidden_size,output_size)

b2 = np.random.rand(output_size)

for i in range(iterations):

# feedforward propagation

z1 =,W1) + b1

a1 = sigmoid(z1)

z2 =,W2) + b2

y_pred = sigmoid(z2)

# error calculation phase

error = y_pred – y_train

mse = mean_squared_error(y_train, y_pred)

# backpropagation phase

delta_output = error * sigmoid(z2) * (1 – sigmoid(z2))

dW2 =,delta_output)

db2 = np.sum(delta_output, axis=0)

delta_hidden =, W2.T) * sigmoid(z1) * (1 – sigmoid(z1))

dW1 =, delta_hidden)

db1 = np.sum(delta_hidden, axis=0)

# weight optimization

W1 -= learning_rate * dW1

b1 -= learning_rate * db1

W2 -= learning_rate * dW2

b2 -= learning_rate * db2

# visualize results

if i%100 == 0:

print(f’Iterations: {i} | Error: {mse}’)

plt.plot(range(iterations), mse)

plt.title(‘Mean Squared Error over Iterations’)



Advantages and Disadvantages of Backpropagation:

Backpropagation has proven to be a useful and flexible method for training neural networks.

It has several advantages such as faster and simple algorithm, flexibility in the number of hidden layers and neurons, and compatibility with various activation functions. However, it also comes with limitations such as sensitivity to noisy and irregular data, and input dependency.


Backpropagation algorithm is an essential technique in training neural networks that has become increasingly popular in machine learning applications. By following the steps outlined in this article, we can implement this algorithm in Python and build effective neural networks.

By understanding the potential advantages and disadvantages of this algorithm, we can ensure that its implementation in our models aligns with our objectives and dataset characteristics. Backpropagation algorithm is a crucial technique for training artificial neural networks, and its implementation in Python plays a vital role in machine learning applications.

In this article, we explored the necessary steps of importing libraries, loading the dataset, splitting the dataset into training and testing, initializing hyperparameters, creating helper functions, and building the backpropagation model. Backpropagation has several advantages, but it also comes with limitations, such as sensitivity to noisy and irregular data and input dependency.

By understanding these advantages and limitations, we can use backpropagation to build efficient neural networks that accurately recognize patterns in data.

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