Fundamentals of machine learning and neural networks: Worked Example — Core Machine Learning and AI Knowledge (NVIDIA-Certified Associate: Generative AI LLM)

Fundamentals of Machine Learning and Neural Networks: Worked Example

Understanding the core concepts of machine learning (ML) and neural networks is essential for the NVIDIA-Certified Associate: Generative AI LLM certification. This worked example demonstrates the step-by-step process of training a simple neural network to classify handwritten digits, a classic problem known as the MNIST digit classification task.

Scenario

You are tasked with building a neural network model that can accurately classify images of handwritten digits (0–9). The dataset consists of 28x28 pixel grayscale images, each labeled with the correct digit.

Step 1: Define the Problem and Dataset

• Input: 28x28 pixel images flattened into a 784-dimensional vector.
• Output: One of 10 classes representing digits 0 through 9.
• Goal: Train a model to predict the correct digit label for each input image.

Step 2: Choose the Model Architecture

We select a simple feedforward neural network with one hidden layer:

• Input layer: 784 neurons (one per pixel).
• Hidden layer: 128 neurons with ReLU activation.
• Output layer: 10 neurons with softmax activation to produce class probabilities.

Step 3: Initialize Model Parameters

Randomly initialize weights and biases for each layer. Weights connect neurons between layers, and biases allow shifting the activation function.

Step 4: Forward Propagation

For each input image:

• Calculate the weighted sum of inputs plus bias for the hidden layer.
• Apply the ReLU activation function: ReLU(x) = max(0, x).
• Calculate the weighted sum plus bias for the output layer.
• Apply the softmax function to obtain probabilities for each digit class.

Step 5: Compute Loss

Use the cross-entropy loss function to measure the difference between predicted probabilities and the true label:

Loss = -∑(y_true * log(y_pred))

where y_true is the one-hot encoded true label and y_pred is the predicted probability vector.

Step 6: Backpropagation

Calculate gradients of the loss with respect to weights and biases using the chain rule. This step propagates the error backward through the network to update parameters.

Step 7: Update Parameters

Apply an optimization algorithm such as stochastic gradient descent (SGD) to adjust weights and biases:

• weight_new = weight_old - learning_rate * gradient
• bias_new = bias_old - learning_rate * gradient

Step 8: Iterate Training

Repeat steps 4–7 over multiple epochs (full passes through the training dataset) until the loss converges or accuracy plateaus.

Worked Example Summary

Given: 28x28 pixel images, 10 output classes.

Process:

1. Flatten image to 784-dimensional vector.
2. Forward propagate through hidden layer with ReLU activation.
3. Forward propagate through output layer with softmax activation.
4. Calculate cross-entropy loss.
5. Backpropagate error to compute gradients.
6. Update weights and biases using SGD.
7. Repeat for multiple epochs.

Outcome: The neural network learns to classify handwritten digits with increasing accuracy by iteratively adjusting parameters to minimize loss.

This example encapsulates the fundamental workflow of training a neural network, a core skill validated by the NVIDIA-Certified Associate: Generative AI LLM exam. Mastery of these steps builds a solid foundation for developing and integrating AI-driven applications using large language models and other deep learning architectures.

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