How a Large Language Model (LLM) Works

(A duck‑tastic tour for a bachelor‑level reader)

1. The “Big Brain” in a nutshell

Imagine a giant, super‑smart brain that sits in a server room. That brain is made of layers of mathematical “cells” called neural networks. An LLM (Large Language Model) is just a particular type of neural network that has learned to generate, translate, answer questions, and more—all by reading a huge amount of text from the internet, books, articles, and so on.

Think of it as a student who has read almost every book and article that ever existed, and now can write essays, answer trivia, or even help you solve a math problem. The student learned patterns in the text, not facts about the world. That’s why it can produce creative, plausible sentences but sometimes hallucinate.

2. The building blocks

3. From raw text to a “smart” brain

3.1 Tokenization & Embeddings

1. Tokenize the training text: “The quick brown fox.” → [“The”, “quick”, “brown”, “fox”].
2. Map each token to a high‑dimensional vector:

"The"   → [0.12, -0.45, 0.78, …]
"quick" → [0.34, 0.21, -0.56, …]

1. (Each number is a dimension; typical models use 768‑dim or 2048‑dim vectors.)

Math shortcut: Instead of doing complex calculus, think of these vectors as color codes that encode how “similar” two words are. The more two vectors line up, the more the words are related.

3.2 Attention: “Which words matter?”

The core trick of transformers is self‑attention. For each position i in the sentence, the model calculates a weighted sum of every other position j:

Attention(i) = Σ (softmax(score(i,j)) × value(j))

• Score(i,j): how much token i should pay attention to token j.
• Softmax: turns raw scores into probabilities that sum to 1.
• Value(j): the vector representation of token j.

Simplified math:
Imagine you have a list of 10 notes. For each note, you look at every other note, give each a “like” score (0–10), turn the likes into percentages, then average the notes weighted by those percentages. The result tells you how the whole list influences that one note.

3.3 Feed‑forward and stacking layers

After attention, the model passes the result through a small feed‑forward network (two linear layers with a ReLU in between). This refines the information. Then you stack many of these Transformer blocks (e.g., 12, 24, 96 layers). The deeper you go, the more abstract the patterns become—much like going from spelling to sentence structure to entire stories.

3.4 Training: “Learning from mistakes”

During training, the model sees a sentence and is asked to predict the next word.

1. Forward pass: Compute predicted probabilities for each possible next token.
2. Loss: Compare prediction to the true next token using cross‑entropy loss (a measure of error).
3. Backpropagation: Compute gradients (how to change weights to reduce error).
4. Optimization (Adam): Update the millions or billions of parameters (weights).

This cycle repeats billions of times.

Math hint:
Instead of solving complicated integrals, think of gradient descent as sliding a ball down a hill: each step takes the ball a little closer to the bottom (the optimum weights).

4. Inference: “Now what?”

When you ask the LLM a question, it runs the text through the same layers, but this time generating tokens one by one:

1. Prompt → tokenized → embedded.
2. Model processes it, outputs a probability distribution for the next token.
3. Pick a token (greedy, nucleus sampling, top‑k, etc.).
4. Append token, repeat until an end‑of‑sentence token appears or you hit a length limit.

5. The duck’s side‑story

Picture a quacking duck named Quackly floating in a pond that is actually the LLM’s training data lake.

1. Quackly dives in and finds a pile of words (tokens).
2. It flips through the pile, picks a handful of shiny ones (high‑attention scores).
3. It quacks (produces) a sentence that sounds like a duck‑ish poem.
4. The pond shouts back: “Nice quack, try this next!”
5. Quackly learns to improve her quack by adjusting her quack‑vectors—just like the model learns to adjust its weights.

Lesson: Even a playful duck can help illustrate how attention and learning work: she selects relevant information, adjusts based on feedback, and becomes better at quacking—just like an LLM becoming better at language.

Quick recap

Bottom line: An LLM is a giant mathematical machine that learns patterns in text by repeatedly correcting itself. It doesn’t “understand” the world like a human, but it has become extremely good at producing fluent, contextually appropriate language—thanks to transformers, attention, and a little quack‑inspired creativity.

Happy duck‑watching—and feel free to ask more questions! 🦆