How Does an LLM Work? The Math, Attention, and Architecture Explained

Beyond the Magic: The Engineering Behind LLMs

To non-engineers, interacting with a Large Language Model can feel like talking to a sentient mind. But to software engineers and computer scientists, an LLM is an intricate pipeline of linear algebra, matrix multiplications, and statistical sampling.

This article explains the internal mechanics of how an LLM actually works—from raw text to vector embeddings, self-attention calculations, and output token generation.

For related concepts, see what is an LLM and our guide to transformer architecture explained simply.

The Step-by-Step Inference Pipeline

When you submit a prompt to an LLM, the request travels through a four-stage computational pipeline:

Raw Text Input
      ↓
1. Tokenization (Text → Token IDs)
      ↓
2. Vector Embedding (Token IDs → High-Dimensional Vectors)
      ↓
3. Transformer Layers (Multi-Head Self-Attention + Feedforward)
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4. Logits & Softmax Sampling (Probabilities → Next Token ID)

1. Tokenization: Converting Text into Numbers

Neural networks cannot process strings of text; they only understand numbers.

The tokenizer breaks words down into sub-word tokens using algorithms like Byte-Pair Encoding (BPE).

• The sentence "Building web applications is fun" becomes an array of token IDs: [4821, 3912, 6421, 318, 1205].
• Learn more in our dedicated guide on how AI tokens work.

2. Embeddings: Mapping Meaning in Vector Space

Each token ID is mapped to a dense vector in high-dimensional space (often 4,096 to 12,288 dimensions).

In this mathematical space, geometric distance reflects semantic meaning:

• Tokens with similar meanings ("cat" and "kitten") have vectors pointing in similar directions.
• Positional encodings are added to each vector so the model knows where each word appears in the sentence.

3. Self-Attention: Understanding Context

The core innovation of the Transformer is the Self-Attention Mechanism.

Consider the sentence:

What does the word "it" refer to? The developer, or the database?

• Self-attention calculates mathematical attention scores between "it" and every other word.
• The attention score between "it" and "database" is high.
• The attention score between "it" and "developer" is low.

By computing attention across multiple "heads" in parallel, the model simultaneously tracks grammatical relationships, pronouns, verb tenses, and logical dependencies.

4. Output Sampling: Turning Math into Text

After passing through dozens of transformer layers, the model outputs logits—raw numerical scores for every word in its vocabulary (typically 50,000 to 128,000 tokens).

A Softmax function converts logits into percentage probabilities. The model then samples the next token based on your configured Temperature:

• Temperature = 0.0: Greedy decoding. The model always picks the #1 most probable token (ideal for code and math).
• Temperature = 0.7: Introduces diverse token choices (ideal for creative writing).

The Stateless Nature of LLMs

A vital engineering concept is that LLMs have no ongoing memory. They do not "remember" what you typed ten minutes ago. Every time you submit a new message in a chat, the entire previous transcript is re-encoded and processed from scratch.

This explains why long conversations consume increasing token quotas, as detailed in our guide on Claude usage limits explained.

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