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Understanding intelligent systems from first principles.

Apr 13

The Chain Rule & Backpropagation

This concept of multiplying derivatives backward through a chain of equations is called Backpropagation.

#Backpropagation (Single Node)#The Chain Rule#Backpropagating a Linear Regressor
Apr 12

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.

#Gradient Descent (Mathematical Gravity)#The Derivative#The Gradient Descent Loop
Apr 11

The Capstone: The Batch-Processing Regressor

Why do we go through all the trouble of building matrices? Parallelization.

#The Batch Regressor#The Batch System#Building the BatchLinearRegressor
Apr 10

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.

#Multicollinearity#Linear Dependence#Implementing get_column
Apr 9

Transposition & Shapes: Aligning the Math

Why is transposition so critical in machine learning? It is the ultimate "adapter cable" for matrix multiplication.

#Aligning the Math#The Matrix Transpose#Implementing the T Property
Apr 8

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.

#Deep Learning & Hidden Layers#Multiplying Matrices#Implementing dot_matrix
Apr 7

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.

#The Batch Forward Pass#Matrix-Vector Multiplication#Implementing dot_vector
Apr 6

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.

#Manipulating the Dataset#Scaling and Shifting Matrices#Implementing __add__ and __mul__
Apr 5

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.

#The Design Matrix#Matrices and Dimensions#Building the Matrix Class