Mathematics Behind Backpropagation | Theory And Python Code

Implement Backpropagation & Gradient Descent from scratch in your own neural network, then code it Without any Libraries

What you'll learn

Understand and Implement Backpropagation by Hand and Code

Understand the Mathematical Foundations of Neural Networks

Build and Train Your Own Feedforward Neural Network in Python without any Libraries

Explore Common Pitfalls in Backpropagation

Numerically Calculate Derivatives, Partial Derivatives and Gradients through Examples

Find the Derivatives of Loss Functions and Activation Functions

Undestand What Derivatives are

Visualize Gradient Descent in Action

Implement Gradient Descent by Hand

Use Python to code Multiple Neural Networks

Undertand how Partial Derivatives Work in Backpropagation

Understand Gradients and How they guide Machines to Learn

Learn Why we Use Activation Functions

Understand the Role of Learning Rates in Gradient Descent

Requirements

basic python knowledge

high school mathematics

Description

Unlock the secrets behind the algorithm that powers modern AI: backpropagation. This essential concept drives the learning process in neural networks, powering technologies like self-driving cars, large language models (LLMs), medical imaging breakthroughs, and much more.In Mathematics Behind Backpropagation | Theory and Code, we take you on a journey from zero to mastery, exploring backpropagation through both theory and hands-on implementation. Starting with the fundamentals, you'll learn the mathematics behind backpropagation, including derivatives, partial derivatives, and gradients. We’ll demystify gradient descent, showing you how machines optimize themselves to improve performance efficiently.But this isn’t just about theory—you’ll roll up your sleeves and implement backpropagation from scratch, first calculating everything by hand to ensure you understand every step. Then, you’ll move to Python coding, building your own neural network without relying on any libraries or pre-built tools. By the end, you’ll know exactly how backpropagation works, from the math to the code and beyond.Whether you're an aspiring machine learning engineer, a developer transitioning into AI, or a data scientist seeking deeper understanding, this course equips you with rare skills most professionals don’t have. Master backpropagation, stand out in AI, and gain the confidence to build neural networks with foundational knowledge that sets you apart in this competitive field.

Overview

Section 1: What We're Going to Learn

Lecture 1 What is this Course

Section 2: Course Resources

Lecture 2 Course Resources

Section 3: Neural Networks, Derivatives, Gradients, Chain Rule, Gradient Descent and more

Lecture 3 Introduction to Our Simple Neural Network

Lecture 4 Why We Use Computational Graphs

Lecture 5 Conducting the Forward Pass

Lecture 6 Roadmap to Understanding Backpropagation

Lecture 7 Derivatives Theory

Lecture 8 Numerical Example of Derivatives

Lecture 9 Understanding Partial Derivatives

Lecture 10 Understanding Gradients

Lecture 11 Understanding What Partial Derivatives Do (Example)

Lecture 12 Introduction to Backpropagation

Lecture 13 Understanding the Chain Rule (Optional)

Lecture 14 Gradient Derivation of the Mean Squared Error Loss Function

Lecture 15 Visualizing the Loss Function + Gradients

Lecture 16 Using the Chain rule to Calculate the Gradient of w2

Lecture 17 Using the Chain Rule to Calculate the Gradient of w1

Lecture 18 Visualizing Gradient Descent

Lecture 19 Introduction to Gradient Descent

Lecture 20 Understanding the Learning Rate (Alpha)

Lecture 21 Moving in the Opposite Direction of the Gradient

Lecture 22 Calculating Gradient Descent by Hand

Lecture 23 Coding our Simple Neural Network Part 1

Lecture 24 Coding our Simple Neural Network Part 2

Lecture 25 Coding our Simple Neural Network Part 3

Lecture 26 Coding our Simple Neural Network Part 4

Lecture 27 Coding our Simple Neural Network Part 5

Section 4: Implementing Our Advanced Neural Network By Hand + Python

Lecture 28 Introduction to Our Advanced Neural Network

Lecture 29 Conducting the Forward Pass

Lecture 30 Getting Started with Backpropagation

Lecture 31 Getting the Derivative of the Sigmoid Activation Function (Optional)

Lecture 32 Implementing Backpropagation with the Chain Rule

Lecture 33 Understanding How w3 Affects the Final Loss

Lecture 34 Calculating Gradients For Z1

Lecture 35 Understanding How w1 & w2 Affect the Loss

Lecture 36 Implementing Gradient Descent By Hand

Lecture 37 Coding our Advanced Neural Network Part (Implementing Forward Pass + Loss)

Lecture 38 Coding our Advanced Neural Network Part 2 (Implement Backpropagation)

Lecture 39 Coding our Advanced Neural Network Part 3 (Implement Gradient Descent)

Lecture 40 Coding our Advanced Neural Network Part 4 (Training our Neural Network)

Data Scientists who want to deepen their understanding of the mathematical underpinnings of neural networks.,Aspiring Machine Learning Engineers who want to build a strong foundation in the algorithms that power AI.,Software Developers looking to transition into the exciting world of machine learning and AI.,Students and Enthusiasts eager to learn how machine learning really works under the hood.,Professionals aiming to stay competitive in the era of LLMs and advanced AI by mastering skills beyond basic frameworks.