Author(s): Gurpreet Deol

Originally published on Towards AI.

Originally published on MLHub, where you can read the full article (54 min read) for free. This is the first part.

Most people learn the maths of machine learning from one of two places, and both let them down in opposite ways.

This article explains how to learn the math behind modern AI by bridging theory and practice: derive results step-by-step in plain English, then implement the computations in NumPy and numerically verify the derivations (and use the code as a check when algebra and results disagree). It frames the content as Part 5 of the MLHub series and sets up a NumPy-first workflow (no GPU, repeatable RNG, float64 for accuracy), establishes conventions for shapes of vectors/matrices and linear maps, and introduces key building blocks like dot products (similarity), cosine similarity, and how matrices represent linear transformations. It then walks through the dense layer formulation as X @ W + b using broadcasting, discusses the computational “cost” of matrix multiplication and why operation order matters, and culminates by deriving linear regression two ways—via normal equations (least squares geometry and practical numerical guidance like avoiding explicit matrix inverses) and foreshadowing gradient descent and gradient-checking in later parts.

Read the full blog for free on Medium.

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Published via Towards AI