The Chain Rule & Backpropagation
This concept of multiplying derivatives backward through a chain of equations is called Backpropagation.
The Derivative & Gradient Descent
This concept is the core intelligence of every neural network in existence, from the simplest regressor to Large Language Models. It is called Gradient Descent.
The Capstone: The Batch-Processing Regressor
Why do we go through all the trouble of building matrices? Parallelization.
The Curse of Multicollinearity: Redundant Data
Why is linear dependence a problem for Artificial Intelligence? In data science, this concept is called Multicollinearity, and it destroys models.
Transposition & Shapes: Aligning the Math
Why is transposition so critical in machine learning? It is the ultimate "adapter cable" for matrix multiplication.
Matrix-Matrix Multiplication: Deep Learning & Hidden Layers
Why do we need to multiply two matrices together? This is the exact mathematical operation that unlocks Deep Learning.
Matrix-Vector Multiplication: The Batch Forward Pass
In The Capstone: Object-Oriented ML Architecture, to make predictions for 3 houses, we had to run our predict method 3 separate times. In Python, this requires a for loop, which is notoriously slow for large datasets.
Matrix Addition & Scalar Multiplication
Why do we need these operations? In machine learning, we rarely use raw data exactly as it comes to us. We need to preprocess it so our neural networks can digest it effectively.
What is a Matrix? Representing Datasets
In Week 1, we built an engine that could look at a single house (a vector) and predict a price. But in the real world, we don't train AI on one house at a time; we train it on thousands or millions of houses simultaneously.