Stay Inquisitive!

I’m a firm believer in the Feynman technique, the idea that teaching is the best way to learn. This blog is my space to apply that method by breaking down complex ideas and explaining them in simple, intuitive terms. It helps me reinforce my own understanding, and I hope it helps you too. Thanks for stopping by, and happy reading!

Neural Networks: A History of an Idea

Deep Learning

A history of the idea behind neural networks, from Plato’s associationism and Bain’s 1873 claim that the information is in the connections, through the McCulloch-Pitts neuron, Turing’s unorganised machines, Hebb’s rule and Rosenblatt’s perceptron, to the XOR wall and the three senses in which a multi-layer perceptron is universal.

May 21, 2026
69 min

Support Vector Machines

Machine Learning
Supervised Learning
Mathematics

A first-principles tour of support vector machines: from the intuition of a maximum-margin classifier, through functional and geometric margins, the optimal margin classifier, Lagrange duality and the KKT conditions, the dual form that exposes support vectors and inner products, kernels, the soft margin and hinge loss, and finally the SMO algorithm that solves it all.

May 15, 2026
61 min

Kernel Methods

Machine Learning
Supervised Learning
Mathematics

A first-principles tour of kernel methods: from feature maps and polynomial regression, through the kernel trick that hides an infinite-dimensional feature space behind a cheap function, to Mercer’s theorem, the closure rules that let you build kernels from kernels, and the reach of the kernel idea.

May 10, 2026
44 min

Generative Learning: Gaussian Discriminant Analysis and Naive Bayes

Machine Learning
Supervised Learning
Mathematics

A first-principles tour of generative classification: instead of drawing the decision boundary directly, we learn what each class looks like and let Bayes’ rule hand us the boundary. Covers the multivariate Gaussian, Gaussian discriminant analysis, Naive Bayes, Laplace smoothing, and the Bernoulli vs multinomial event models.

May 5, 2026
42 min

The Exponential Family and Generalized Linear Models

Machine Learning
Supervised Learning
Mathematics

Linear regression and logistic regression are not two separate inventions; they are two turns of one crank. This post builds the exponential family and generalized linear models from first principles, shows why the sigmoid is inevitable, solves a brand-new problem (counting customers) almost for free, and derives softmax regression, all from a single recipe.

Apr 30, 2026
34 min

Introduction to RAG

GenAI
RAG

A first-principles introduction to Retrieval Augmented Generation: the four problems with LLMs, why in-context learning alone is not enough, and how RAG assembles just the right context to ground an LLM’s answers.

Apr 20, 2026
30 min

Classification, the Perceptron, and Logistic Regression

Machine Learning
Supervised Learning
Mathematics

A first-principles walk from binary classification to the perceptron, logistic regression, and Newton’s method, told as the story of a single object: the decision boundary, drawn ever more intelligently.

Apr 18, 2026
50 min

Independence: When One Event Tells You Nothing About Another

Probability
Mathematics

We build the concept of independence from scratch, starting with three tosses of a biased coin. Along the way we untangle independence from disjointness, see how conditioning can both destroy and create independence, distinguish pairwise from full independence, and close with the king’s sibling puzzle, which shows that the answer to a probability problem can depend on assumptions you didn’t even realize you were making.

Apr 17, 2026
22 min

Conditional Probability, the Multiplication Rule, Total Probability, and Bayes’ Rule

Probability
Mathematics

What happens to our probabilities when the world tells us something new? A first-principles tour of conditional probability and the three tools that follow from it: the multiplication rule, the total probability theorem, and Bayes’ rule, told through a single running radar example.

Apr 10, 2026
23 min

Linear Algebra, Part 2: Elimination, Inverses, and A = LU

Linear Algebra
Mathematics

The second post in a story-driven linear algebra series following Gilbert Strang’s MIT 18.06 lectures. We turn the picture-based solving of Part 1 into a systematic algorithm, elimination, discover that each step is a matrix multiplication, survey the five ways to multiply matrices, meet the inverse and the singular matrices that have none, and uncover the surprise that solving a system is secretly factoring its matrix into A = LU (and A = LDU). We finish with the permutations that handle row swaps and the transpose that gives us symmetric matrices.

Mar 29, 2026
39 min

Linear Algebra, Part 1: The Geometry of Linear Equations

Linear Algebra
Mathematics

The opening post in a story-driven linear algebra series following Gilbert Strang’s MIT 18.06 lectures. We meet the central problem Ax = b through two complementary pictures: rows (lines crossing) and columns (combining vectors), and uncover the one question that drives the whole subject.

Mar 26, 2026
13 min

Probability Models and Axioms

Probability

Building the foundations of probability from scratch: sample spaces, events, probability axioms, and the discrete and continuous uniform laws.

Mar 25, 2026
26 min

Linear Regression

Machine Learning
Supervised Learning
Mathematics

A first-principles introduction to linear regression, from eyeballing a line on a scatter plot to deriving the closed-form solution, its probabilistic justification, and locally weighted (non-parametric) regression.

Mar 22, 2026
51 min

Linear Algebra for Machine Learning: A First-Principles Guide

Linear Algebra
Mathematics

A comprehensive, story-driven guide to linear algebra, building from concrete examples to the mathematical tools that power machine learning. Covers matrix operations, eigenvalues, matrix calculus, and least squares.

Mar 10, 2026
82 min

Introduction to Machine Learning

Machine Learning

A rigorous introduction to machine learning, covering its definition, core paradigms, and the role of data, with mathematical notation and intuitive examples.

Dec 24, 2025
20 min

Introduction to APIs

FastAPI

A practical, story-driven introduction to APIs: what they are, how a single request travels end to end, their anatomy, types, protocols (REST, SOAP, GraphQL, gRPC, WebSocket), authentication and authorization, and the full API lifecycle.

Jul 15, 2025
29 min

Network of Sigmoid Neurons

Deep Learning

An exploration of multilayer networks of sigmoid neurons and their ability to approximate any continuous function, illustrating the universal approximation theorem with tower constructions in 1D and 2D.

Jul 3, 2025
8 min

Notational Reference for my Posts

Reference

This post serves as a notational reference in which you can find all the notational conventions I use in my blog posts.

Jul 1, 2025
3 min

Sigmoid Neuron

Deep Learning

An introduction to the sigmoid neuron and logistic activation for real-valued modeling, highlighting probabilistic outputs, differentiability, and gradient descent. Includes a Taylor series intuition, a toy example, and pseudocode for parameter updates.

Jun 26, 2025
23 min

Hadoop Distributed File System

Data Engineering

An in-depth guide to the Hadoop Distributed File System (HDFS), covering its architecture, blocks, replication, fault tolerance, rack awareness, and how read/write operations are handled for scalable and reliable big data storage.

Jun 25, 2025
31 min

Hadoop

Data Engineering

An overview of Hadoop, its core properties, and its ecosystem of components like HDFS, MapReduce, YARN, Hive, Pig, and more. This post explains how Hadoop enabled distributed storage and processing, and why it remains foundational for modern big data technologies.

Jun 24, 2025
5 min

Network of Perceptrons (MLP)

Deep Learning

An exploration of multilayer perceptrons (MLPs) and their ability to implement any Boolean function, including non-linearly separable ones like XOR. This post illustrates how hidden layers expand representation power and generalizes the idea to networks with more inputs.

Jun 23, 2025
9 min

Perceptron

Deep Learning

A deep dive into the perceptron, a fundamental binary classifier that extends the McCulloch-Pitts neuron with learnable weights and bias. This post explains its working, geometric interpretation, learning algorithm, and limitations on non-linearly separable data like XOR.

Jun 14, 2025
26 min

McCulloch-Pitts Neuron

Deep Learning

An introduction to the McCulloch-Pitts neuron, one of the earliest computational models of the brain. This post builds the model from a simple movie-recommendation scenario, then shows how it implements Boolean functions and reveals its geometric nature as a linearly separable classifier.

Jun 12, 2025
16 min
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