How Tokenization Works#

Tokenization doesn’t simply split text by spaces. Modern language models use sophisticated algorithms like Byte-Pair Encoding (BPE) that intelligently break text into subword units called tokens.

Example: The phrase “understanding tokenization” might be split into:

• ["under", "standing", "token", "ization"]

Or even more granularly:

• ["und", "er", "stand", "ing", "token", "iz", "ation"]

Why This Matters for Prompt Engineering#

Understanding tokenization helps explain why certain prompt structures work better than others. When you write a prompt, you’re not just communicating with the AI—you’re providing a sequence of tokens that the model will process mathematically.

Key Insights:

• Token Efficiency: Shorter, more common words typically use fewer tokens
• Context Windows: Models have token limits (e.g., 4,096 or 8,192 tokens), not word limits
• Prompt Optimization: Understanding tokenization helps you maximize information density within context limits

The Mathematics of Next-Token Prediction#

When you input a prompt, the model:

1. Processes the token sequence: Converts your text into numerical representations
2. Calculates probabilities: For each possible next token in its vocabulary (typically 30,000-50,000 tokens)
3. Selects the next token: Based on probability distribution and sampling strategy
4. Repeats the process: Using the new token sequence to predict the following token

Example Process:

1
Input: "The capital of France is"
2
Model calculates:
3
- "Paris" (85% probability)
4
- "located" (8% probability)
5
- "known" (3% probability)
6
- Other tokens (4% probability)

How Prompts Influence Probability Distributions#

This is where prompt engineering becomes scientific rather than magical. Your prompt doesn’t just provide information—it shapes the probability landscape for all subsequent tokens.

Strategic Implications:

• Context Setting: Earlier tokens in your prompt influence the probability of later tokens
• Priming Effects: Specific words or phrases can bias the model toward certain types of responses
• Chain-of-Thought: Step-by-step reasoning prompts work because they increase the probability of logical, sequential thinking patterns

Understanding Self-Attention#

Self-attention enables models to weigh the importance of different elements in an input sequence and dynamically adjust their influence on the output. This is especially crucial for language processing, where the meaning of a word can change based on its context.

Analogy: Imagine reading a complex sentence where you need to remember what “it” refers to. Your brain automatically looks back through the sentence to find the relevant noun. Attention mechanisms work similarly—they allow the model to “look back” and focus on relevant previous tokens when predicting the next one.

The Mathematics of Attention#

Attention mechanisms use three key components:

• Queries (Q): What information is the model looking for?
• Keys (K): What information is available in the sequence?
• Values (V): The actual information content

The attention score determines how much focus each token should receive when processing the current position.

Multi-Head Attention: Parallel Processing Power#

Transformer models use “multi-head attention” to compute multiple attention operations in parallel, each focusing on different types of relationships between tokens.

Why This Matters: This parallel processing allows models to simultaneously track multiple types of dependencies—grammatical relationships, semantic connections, and logical flows—all at once.