In the architecture of a deep neural network, activation functions are the crucial component that breathes life into the model. Without them, even the deepest network would be nothing more than a s...

How Bigtable's lexicographic row keys drive every schema decision, and how Spanner delivers strongly consistent global SQL without escaping CAP.

A decision framework for picking data stores across an ML system, from training data in object storage to online features under a p99 budget.

When we ask an LLM a question, it doesn’t just “know” the answer. At each step it produces a score for every possible next token, one step at a time. But how it turns those scores into an actual ch...

Part 1 and Part 2 covered the algorithms and the XGBoost mathematics. This final part is practical: the general boosting concepts that apply to any library (feature importance, early stopping), and...

Part 1 built gradient boosting as gradient descent in function space. XGBoost keeps that idea but rebuilds the objective: a regularized loss, a second-order (Newton) approximation, and a closed-for...

Boosting answers a deceptively simple question: can a committee of weak learners, each barely better than a coin flip, add up to one strong model? This series works through the answer. Part 1 cover...

In Part 1 we built a single Decision Tree - and saw how readily it overfits. That sets up a natural thought: “If one tree is good, surely a whole forest is better?” That intuition is absolutely ri...

Imagine playing a game of “20 Questions.” We are trying to guess an object, and we can only ask yes/no questions. To win quickly, we wouldn’t ask, “Is it a 1994 Ford Taurus?” right away. We’d ask b...

Principal Component Analysis (PCA) is fundamentally a geometric optimization problem: finding the directions that capture the maximum variance in a dataset. This article derives the core equations ...