Neural Networks and Deep Learning: Principles and MNIST Example

This article discusses the latest developments in generative AI, including GPT‑5 and AI software engineers, and examines their potential impact on national competition and individual careers.

Sam Altman revealed details of GPT‑5, claiming a huge performance boost.

The first AI software engineer demonstrates planning, DevOps, and full‑project scanning abilities.

The author argues that AI technology is not a black box; its data, storage, and computation are deterministic and explainable.

The tutorial is organized into three parts: (1) a simple network to illustrate the basic principles of neural networks and deep learning; (2) a real‑world network example for hands‑on feeling; (3) a common question that leads to more complex networks.

Neural network fundamentals – A neural network learns general patterns from the training set and stores them in parameters. Each neuron has N+1 parameters (weights and bias). Learning is a deterministic process that moves from a random point in high‑dimensional parameter space toward the minimum loss.

Example of a linear regression network:

output = activation_function(W * X + b)

When the activation function is linear, the output simplifies to output = W * X + b .

For a network with two inputs and two hidden neurons, the total number of parameters is 9 (weights and biases).

Activation functions – Non‑linear functions such as ReLU, Sigmoid, and Softmax enable the model to fit complex problems. Softmax converts the output layer into a probability distribution.

Deep learning process – The training loop consists of:

Initialize parameters (e.g., random m and b).

Forward propagation to compute predictions.

Compute loss (e.g., Mean Squared Error).

Back‑propagation to obtain gradients.

Update parameters with gradient descent ( m = m - lr * ∂L/∂m ).

Repeat for multiple epochs, monitoring training and validation accuracy.

The article uses the MNIST handwritten‑digit dataset as a case study. After loading and visualizing the data, the pipeline includes flattening, normalizing, and one‑hot encoding the labels, building a model with two hidden layers of 512 ReLU units and a Softmax output, compiling with categorical cross‑entropy, and training while observing accuracy.

Overfitting is identified when training accuracy is high but validation accuracy drops. Solutions include using more appropriate architectures (e.g., CNNs, RNNs) and regularization techniques.

The material is based on Nvidia’s “Getting Started with Deep Learning” course.