02 - Differential Calculus for DL: Gradients and Backpropagation

How neural networks learn: partial derivatives, chain rule (the core), backpropagation step-by-step. NO limits and epsilon-delta—visual intuition of gradients. Computational graphs, automatic differentiation. Manual NumPy implementation, why PyTorch uses autograd.

What you'll learn

• Derivative: measures rate of change, indicates the function slope
• Gradient \nabla L: points in the direction of steepest ascent of the loss
• Gradient descent: \theta \leftarrow \theta - \eta \nabla L - move opposite to the gradient
• Chain rule: allows computing gradients through function compositions
• Backpropagation: applying the chain rule to the network's computational graph

This article is part of the Math for AI series on federicocalo.dev.

Read the full article

The complete article (17 min read) with code examples, diagrams, and practical exercises is available here:

➡️ 02 - Differential Calculus for DL: Gradients and Backpropagation

https://federicocalo.dev/en/blog/differential-calculus-deep-learning-gradients-backpropagation

By Federico Calò — Software Developer & Technical Writer