How LLMs Actually Work

a from-scratch explainer

How LLMs Actually Work

From your first vector to attention, training, and LoRA, with no math background needed.

Start with Chapter 1 →

(The trailer starts muted — tap the speaker icon for narration. Chapter videos play with sound.)

How LLMs actually work · narrated, with captions.

Hi, I'm Sean Egan, a Navy information warfare officer and research scientist. I built this book for colleagues and friends who want to know how a language model works.

We'll follow the real equations and check some by hand. You need no math background. Part I builds the tools, starting with an arrow on a page. Then we follow text into the model, watch attention combine information, and see how training changes its numbers.

New to this? Start with Chapter 1 and take your time. Already know linear algebra? Start at Part II; the prerequisite links bring you back whenever you need a refresher. Watch the videos, drag the interactives, get a pencil. We'll work through this together.

How to read

Three ways to make an idea stick
ToolUse it to
VideosWatch the idea move.
InteractivesChange one thing and see what follows.
Worked examplesCheck the arithmetic with a pencil.

Part I

The Math You Need

    1Numbers That PointVectors: arrows, coordinates, and why direction is information6 min 2Measuring SimilarityThe dot product: one number that says how much two arrows agree7 min 3Grids That TransformMatrices: machines that turn one vector into another8 min 4Functions and Curvesf(x), exponentials and logarithms: the shapes the math is made of7 min 5Slopes and DescentDerivatives: which way is downhill, and how steep?8 min 6Chance and ChoiceProbability: spreading belief across possibilities7 min

Part II

Inside an LLM

    7Text Becomes NumbersTokens: chopping language into countable pieces6 min 8Meaning as DirectionEmbeddings: every token becomes an arrow, and nearby arrows mean similar things6 min 9The Prediction GameOne job: guess the next token7 min 10AttentionHow words look at each other9 min 11The TransformerStacking attention into a thinking machine7 min

Part III

How It Learns

    12Measuring WrongnessLoss: turning 'bad guess' into a single number7 min 13Rolling DownhillGradient descent: learning as finding low ground6 min 14Blame Flows BackwardBackpropagation: how millions of weights each learn their share6 min 15The Training RunTrillions of tokens, thousands of GPUs, one falling curve5 min 16From Parrot to PartnerFine-tuning, RLHF, and how a text predictor becomes an assistant6 min 17Why It Makes Things UpHallucination: no credit for silence, and recall is generation9 min

Part IV

Beyond the Basics

    18LoRATeaching a giant model new tricks by training 1% of it7 min 19Inference, EfficientlyKV cache, context windows, and quantization8 min 20RAG and Vector SearchEmbeddings at work: giving the model a library card7 min 21So… What Is AI/ML?Zooming out: LLMs are one species in a big family5 min