Calculus Essentials for Machine Learning
Chapter 1: Introduction: Why Calculus Matters in Machine Learning
Functions and Models in ML
The Concept of Optimization in ML
Measuring Change: The Role of Derivatives
Calculus as a Tool for Understanding Algorithms
Quiz for Chapter 1
Chapter 2: Single-Variable Calculus: Derivatives and Optimization
Understanding Limits: The Foundation
Defining the Derivative
Common Differentiation Rules
Higher-Order Derivatives
Finding Minima and Maxima using Derivatives
Application: Simple Cost Function Optimization
Hands-on Practical: Calculating Derivatives with Python
Quiz for Chapter 2
Chapter 3: Multivariable Calculus: Gradients and Direction
Functions of Multiple Variables
Partial Derivatives
The Gradient Vector
Directional Derivatives
The Hessian Matrix
Multivariable Optimization Concepts
Hands-on Practical: Computing Gradients with NumPy
Quiz for Chapter 3
Chapter 4: Gradient Descent Algorithms
The Intuition Behind Gradient Descent
The Gradient Descent Algorithm Steps
The Learning Rate Parameter
Batch Gradient Descent
Stochastic Gradient Descent (SGD)
Mini-batch Gradient Descent
Challenges: Local Minima and Saddle Points
Hands-on Practical: Implementing Simple Gradient Descent
Quiz for Chapter 4
Chapter 5: The Chain Rule and Backpropagation
Revisiting the Chain Rule for Single Variables
The Chain Rule for Multivariable Functions
Introduction to Neural Networks as Composite Functions
Backpropagation: Applying the Chain Rule
Calculating Gradients for Weights and Biases
Computational Graphs
Hands-on Practical: Manual Backpropagation Example
Quiz for Chapter 5
Backpropagation: Applying the Chain Rule
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- Learning representations by back-propagating errors, David E. Rumelhart, Geoffrey E. Hinton, Ronald J. Williams, 1986 Nature, Vol. 323 (Springer Nature) DOI: 10.1038/323533a0 - Presents the backpropagation algorithm as an efficient method for computing gradients in multi-layer neural networks, significantly advancing their training.
- Deep Learning, Ian Goodfellow, Yoshua Bengio, Aaron Courville, 2016 (MIT Press) - A comprehensive textbook where Chapter 6 covers deep feedforward networks, including a thorough mathematical derivation and explanation of backpropagation.
- Neural Networks and Deep Learning, Michael A. Nielsen, 2015 (Determination Press) - Provides a clear, step-by-step explanation of how backpropagation works, making the underlying calculus intuitive and accessible.
- Backpropagation in Neural Networks (CS231n Convolutional Neural Networks for Visual Recognition), Stanford University CS231n Course Staff, 2024 - These course notes offer a detailed and practical explanation of backpropagation, often using vectorized notation relevant for modern deep learning frameworks.