Neural Networks: The Building Blocks of Deep Learning
Introduction
You’ve probably heard about Neural Networks — it’s the backbone of many modern AI systems, from facial recognition to self-driving cars. But what exactly are they, and how do they work? In this blog, we’ll break down the basics of neural networks, explain how they make predictions, and dive into the concept of backpropagation, the key to training neural networks.
Let’s start by exploring the foundation of Neural Networks and how they function, step by step.
What is a Neural Network?
A Neural Network is a set of algorithms inspired by the human brain that is designed to recognize patterns. It consists of layers of interconnected nodes (neurons), where each node mimics the functioning of biological neurons.
The simplest type of neural network is called a Single-Layer Perceptron, which consists of:
- Input layer: Takes in features from the dataset.
- Output layer: Produces a prediction.
- Weights and Biases: Adjust values to make predictions more accurate.
For deeper learning tasks, we stack multiple hidden layers between the input and output layers, creating a Multi-Layer Perceptron (MLP) or Deep Neural Network.
How Does a Neural Network Work?
Let’s break it down mathematically, starting with a one-layer neural network. Imagine we have three input features, a single hidden layer with two neurons, and one output. Here’s how it works:
Step 1: Input and Weights
Each input node x is connected to each neuron with a weight www, which determines how much that input affects the final prediction. The network multiplies each input by its weight:
x1,x2,x3 are the features, w1,w2 and w3 are it’s respective co-efficients and b is the bias added to the network.
You might think this actually looks like a linear regression model. Yes, you are absolutely correct! The basic concept of Neural Network is very similar to that of the linear regression model.
But the next question that arises in your mind is, if that’s how Neural Network works, how does it find non-linear and complicated patterns in data? The answer lies in Activation Function.
Step 2: Activation Function
Once the inputs are weighted and summed, we pass them through an activation function. The activation function helps the network learn complex patterns by introducing non-linearity.
There are many activation functions and each serve different purpose. I’ll next try to write a dedicated blog on different activation functions and their purpose, but for now let’s use Sigmoid Activation Function- one of the commonly used activation function.
Now, this is how our network looks like.
Step 3: Output
In a classification problem, the output might be a probability score, which we interpret as the likelihood of a certain class. The final output could be:
Where y is the predicted value (e.g., a probability in classification).
Now, this seems straightforward. But how do we ensure that the network makes accurate predictions? This is where backpropagation comes into play.
What is Backpropagation?
Backpropagation is the process through which a neural network learns from its mistakes. It adjusts the weights and biases to minimize the difference between the predicted output and the actual output, known as the error or loss.
Without backpropagation, the network wouldn’t know how to improve its predictions. The process involves three main steps: feedforward, loss calculation, and backpropagation.
Why Do We Need Backpropagation?
When a neural network makes a prediction, it’s essentially guessing based on the current weights. The first guess might be terrible, but we want the model to learn and improve. Backpropagation allows us to adjust the weights in such a way that the model’s predictions get better over time.
Backpropagation is essential because it gives the network a mechanism to update itself. There are different types of optimization algorithms to minimize the loss by tweaking the weights after each prediction. The common one we know is Gradient Descent.
Mathematical Breakdown of Backpropagation
Let’s explore how backpropagation works mathematically:
Step 1: Loss Function
To evaluate how well the network is performing, we calculate the loss. For regression, we compute MSE as loss function to measure the difference between actual and predicted values.
Step 2: Compute Gradients
To minimize the loss, we compute the gradient of the loss function with respect to each weight. For a weight w, the gradient is:
This equation tells us how the loss changes as we adjust each weight. The chain rule of calculus allows us to break down the gradient computation into parts.
Step 3: Update Weights
Once the gradients are computed, the weights are updated using Gradient Descent. The formula for updating a weight w is:
The smaller the learning rate, the more gradual the changes, which can help prevent the model from overshooting the optimal solution.
Step 4: Repeat
We repeat this process of forward pass, calculating loss, backpropagation, and updating weights across multiple iterations (called epochs). Over time, the model converges as it minimizes the loss, ultimately improving the accuracy of its predictions.
Conclusion: The Power of Neural Networks in Regression
In regression problems, neural networks optimize their predictions by minimizing the Mean Squared Error (MSE). The backpropagation algorithm ensures that the network gradually adjusts its weights to reduce this error by applying the chain rule and using Gradient Descent to update the weights.
By understanding how neural networks perform regression and how backpropagation plays a key role in minimizing prediction errors, you are now equipped with the knowledge to tackle more complex machine learning challenges!
