Behind the Scenes: A Simple Guide to the Math Powering Neural Network Training

Article on Medium

Let's take a closer look at the math stuff in neural network training and see how it actually works in the real world. We'll break down the basics that make this technique so useful for building deep models.

In neural networks, each neuron performs a mathematical operation. During backpropagation, we use a method called gradient descent to adjust the parameters (weights) of these neurons to minimize the error in the network's predictions. Here's how it works mathematically:

Forward Pass: The input data is passed through the network, and for each neuron, we calculate a weighted sum of its inputs, apply an activation function (like sigmoid or ReLU), and pass the result to the next layer. This process continues through the layers until we get the network's output.

Error Calculation: We compare the network's output to the actual target values to calculate the error. This error is typically measured using a loss function, such as Mean Squared Error (MSE) for regression tasks or Cross-Entropy for classification.

Backward Pass (Backpropagation): This is where the magic happens. We calculate the gradient of the error with respect to each weight in the network. This gradient tells us how much each weight contributed to the error. We use the chain rule from calculus to calculate these gradients layer by layer, starting from the output layer and moving backward.

Weight Update: Using the gradients, we update the weights in the network. The idea is to adjust the weights in the direction that reduces the error. Gradient descent is a common optimization technique used here. It adjusts weights proportionally to their influence on the error.

Repeat: Steps 1 to 4 are repeated for many iterations (epochs) until the network's error converges to a minimum, or until a predefined stopping condition is met.

Real-World Application:

A common real-world application of backpropagation is in training deep learning models for tasks like image recognition. Here's how it works in practice:

Image Classification:

Imagine you're building a neural network to identify whether an image contains a human or not. Here's how the technique applies:

Data Preparation: You gather a dataset of labeled human and non-human images.

Model Design: You design a neural network with input neurons for image pixels, hidden layers with various neurons, and an output neuron (1 for human, 0 for non-human).

Forward Pass: You feed an image into the network, and it makes a prediction (e.g., 0.8 for "human" means it's confident the image contains a human).

Error Calculation: You compare the prediction to the actual label (0 or 1) and calculate the error using a loss function.

Backward Pass: Backpropagation calculates how each weight in the network contributed to the error.

Weight Update: The weights are adjusted slightly in the opposite direction of their gradient to reduce the error. This process repeats for many images.

Training: The network goes through thousands or millions of images, gradually getting better at recognizing humans.

Testing: Once trained, the network is tested on new, unseen images to check its accuracy.

In this way, neural networks learn to recognize patterns and make accurate predictions in various applications like image classification, natural language processing, autonomous driving, and more.