A beginner-friendly walkthrough builds understanding of neural networks from the ground up, starting with a single artificial neuron and progressing to weights, biases, activation functions, forward propagation, loss, gradients, backpropagation, and gradient descent. Using only Python and NumPy, it constructs a small neural network from scratch to solve the classic XOR problem, then rebuilds the same network in far fewer lines using PyTorch, comparing the manual math against the framework-assisted approach. It closes with an overview of where neural networks are applied (computer vision, NLP, speech, recommendations, generative AI) and suggests a learning path toward deep learning.
Table of contents
1. What Is a Neural Network?2. Why Are They Called Neural Networks?3. The Three Main Parts of a Neural Network4. What Is a Neuron?5. What Is a Weight?6. What Is a Bias?7. Why Do We Need Activation Functions?8. Building Our First Neuron in Python9. From One Neuron to a Layer10. How Does a Neural Network Actually Learn?11. Predictions and Loss12. What Are Gradients?13. What Is Gradient Descent?14. What Is Backpropagation?15. The Complete Learning Cycle16. Let's Build a Neural Network From Scratch17. Understanding the Network Architecture18. Setting Up the Data19. Creating the Weights and Biases20. The Sigmoid Function21. Forward Propagation22. Calculating the Loss23. Backpropagation in Code24. Updating the Weights25. The Complete NumPy Neural Network26. Testing the Network27. Why Did We Need a Hidden Layer?28. What Happens in a Larger Neural Network?29. Do You Have to Build Neural Networks From Scratch?30. Building the Same Network With PyTorch31. Training the Network With PyTorch32. NumPy vs. PyTorch33. What Is Deep Learning?34. Where Are Neural Networks Used?35. The Whole Process in One Picture36. The Most Important Ideas to Remember37. What Should You Learn Next?Final TakeawayQuestions this post answers
How do I build a simple neural network from scratch using only Python and NumPy?
Initialize weight matrices and biases with numpy, run forward propagation using matrix multiplication (X @ W1 + b1) followed by tanh and sigmoid activations, compute binary cross-entropy loss, then backpropagate gradients manually (dz2 = a2 - y, dW2 = a1.T @ dz2 / len(X), etc.) and update parameters using gradient descent with a learning rate like 0.1 over thousands of epochs. See more from-scratch machine learning walkthroughs curated for developers on daily.dev.
Why does a neural network need a hidden layer to learn the XOR function?
XOR cannot be represented by a single linear layer because it is not linearly separable, so a hidden layer with a nonlinear activation function like tanh is required to give the network the flexibility to transform inputs into a representation where the output layer can separate the classes. Without that nonlinearity, connecting inputs directly to the output cannot capture the XOR pattern. Developers debugging network architecture choices can follow deep learning explainers on daily.dev.
What is the difference between implementing backpropagation manually in NumPy versus using PyTorch's autograd?
Manually implementing backpropagation in NumPy requires computing every gradient by hand, such as dz2 = a2 - y, dW2 = (a1.T @ dz2) / len(X), and applying the tanh derivative (1 - a1**2), then updating parameters with explicit subtraction. PyTorch automates this with loss.backward() and optimizer.step(), using an optimizer like Adam, reducing the same logic to a handful of lines. Compare framework trade-offs like this by following PyTorch and NumPy discussions on daily.dev.