By Stephen Fishburn in Tokenization —

What Is a Token? The Most Misunderstood Concept in AI

Most people think a token is a word. It's not. Tokens are fragments—the atoms of AI computation. Understanding how language gets broken into machine-digestible pieces reveals the magic.

A token is like the thing you buy and use at the AI county fair, whether Claude, ChatGPT, Gemini, or Lovable. Like the local county fair, you pay for tokens and when you use them up, you're done unless you buy more. Tokens are not only the currency at the fair, exchanged for dollars, but the way AI computes your questions and crafts a reply that is shockingly human.

But what is a token really — and how does it become the foundation of a system that appears to understand us?

🧩 Part 1: The Token Illusion

Most people think a token is a word. It's not. A token is a fragment — a sub-word unit.

Think of making apple pie. You don't start with "apple pie"—you start with ingredients. Flour, butter, apples, cinnamon. Each ingredient is like a token: a fundamental building block that combines with others to create something more complex.

Examples:

  • "ChatGPT" → [Chat, G, PT]
  • "Apple Pie: Outline..." → [Apple, ĠPie, :, ĠOutline, Ġcomprehensive, Ġinstructions, ...]
  • " you're" → [Ġ, you, ', re] (yes, the space is a token)

Tokens are how language gets broken down into machine-understandable pieces. They're not words. They're the atoms of computation—the flour and sugar of language.

🔍 How Tokenization Actually Works

Most modern LLMs (like GPT and Claude) use Byte Pair Encoding (BPE) or similar algorithms. BPE breaks words into frequently occurring subword units, like how a baker might prep ingredients by chopping apples into consistent pieces rather than using whole fruits.

For example:

  • unhappiness might be split into [un, happiness]
  • happiness into [happi, ness]

Let's see this with a real recipe prompt. If you ask an LLM:

"Classic American Apple Pie: Provide comprehensive steps with detailed ingredients including Granny Smith apples, cinnamon, nutmeg, sugar, lemon juice, and a buttery pie crust."

That gets tokenized into something like: ["Classic", "▽American", "▽Apple", "▽Pie", ":", "▽Provide", "▽comprehensive", "▽steps", "▽with", "▽detailed", "▽ingredients", "▽including", "▽Granny", "▽Smith", "▽apples", ",", "▽cinnamon", ",", "▽nutmeg", ",", "▽sugar", ",", "▽lemon", "▽juice", ",", "▽and", "▽a", "▽buttery", "▽pie", "▽crust", "."]

(▽ represents spaces included in tokens)

These subword tokens form the base ingredients of what the model processes. Just as a baker needs consistent measurements, the tokenizer's job is to reduce every input into a vocabulary of subword pieces the model can reliably work with.

🧵 What's with the Ġ symbol?

Some tokenizers, like GPT-2's, use a Ġ (a special character) to mark the beginning of a new word when there's a preceding space. It's like the spaces between ingredients in a recipe—invisible but crucial for organization.

Example with explicit token boundaries:

  • Input: ' you're'
  • Tokens: ["Ġ", "you", "'", "re"] where:
    • "Ġ" = space before word (like the gap between "2 cups" and "flour")
    • "you", "'", "re" = subword parts of "you're"

Modern tokenizers often include spaces within tokens:

  • ' you're' → [" you", "'re"] (space included in first token)
  • 'hamburger' → ["ham", "bur", "ger"] (classic BPE breakdown)

This enables LLMs to generalize across grammar, contractions, and compound words—even when they've never seen the full word before, just like how an experienced baker can improvise with ingredients they've never combined.

🔁 Part 2: What the Model Actually Does

Imagine you're following a recipe, but instead of seeing the whole thing at once, you get one ingredient at a time and have to guess what comes next. That's exactly how an LLM works.

Let's say you give the model our apple pie prompt:

"Classic American Apple Pie: Provide comprehensive steps with detailed ingredients including Granny Smith apples, cinnamon, nutmeg, sugar, lemon juice, and a buttery pie crust."

This becomes a sequence of tokens—[Classic, ĠAmerican, ĠApple, ĠPie, :, ĠProvide, ...]. The model doesn't see "apple pie recipe"—it sees these ingredient-like tokens, one by one.

The entire LLM pipeline is like following a recipe blindfolded:

  1. You input a sequence of tokens (the ingredients you have so far)
  2. The model predicts the next likely token (guesses the next ingredient)
  3. That token gets appended (adds it to the recipe)
  4. Repeat (continues building the dish)

The magic is in how it chooses the next token. After seeing [Apple, ĠPie, :], it might predict ĠFirst or ĠPreheat or ĠFor—all reasonable ways to start recipe instructions. That's where all the math lives.

🧠 Part 3: The Attention Mechanism

The core of a transformer is self-attention. Every token looks at every other token to decide what matters—like a master chef constantly tasting and adjusting, considering how each ingredient affects the others.

When the model sees [Classic, ĠAmerican, ĠApple, ĠPie, :, ĠProvide, Ġcomprehensive, Ġsteps], attention helps it understand that "Classic American" modifies "Apple Pie," that "comprehensive steps" suggests detailed instructions are wanted, and that the colon indicates a structured response is coming.

The formula:

Attention(Q, K, V) = softmax(QKᵀ / √dₖ) × V

Where:

  • Q (query), K (key), and V (value) are projections of the input tokens
  • dₖ is the dimension of the key vectors (used to scale dot products)
  • The × V step produces the final weighted combination of values

This gives the model the ability to weigh which tokens matter most—dynamically, per context. Just like how the word "tart" means something different in "tart apples" versus "strawberry tart."

Attention determines what matters. Next comes the question: how wrong was the guess?

🎯 Part 4: How the Model Learns

Training uses cross-entropy loss. The model learns by trying to minimize the difference between its prediction and the actual next token—like a cooking student getting corrected every time they reach for the wrong ingredient.

If the correct next token is Preheat, and it predicted Mix, it gets penalized. Over millions of examples, it learns the patterns of language the same way a chef learns that certain flavors naturally follow others.

The loss function is:

L = -∑ (yᵢ * log(pᵢ))

Where:

  • yᵢ is the true distribution (usually one-hot: correct token = 1, rest = 0)
  • pᵢ is the predicted probability for each token

🧱 Part 5: How Narratives Form—And Fall Apart

Because LLMs predict one token at a time, the first token steers the second, like how the first ingredient you add to a pan influences everything that follows. The second steers the third. Over time, the model builds a narrative that tries to stay internally consistent—even if the first token was catastrophically wrong.

Let's revisit our apple pie example. When given the prompt "Classic American Apple Pie: Provide comprehensive steps...", the model doesn't retrieve a specific recipe from memory. It constructs one—token by token—based on patterns learned from thousands of similar recipes.

It might start with Preheat, then Ġthe, then Ġoven, then Ġto, then 375, forming instructions that sound grounded in culinary logic. But it's not consulting a cookbook—it's composing a statistically plausible culinary story, ingredient by ingredient, instruction by instruction.

🔥 When the Kitchen Burns Down: The Chaos of Token Generation

But here's what the happy path doesn't show you—token generation is often barely-controlled chaos. The model isn't calmly selecting the perfect next ingredient. It's more like a frantic chef grabbing from probability shelves in a burning kitchen.

The First Token Trap: If the model starts with the wrong direction, everything that follows must make that path sound reasonable. Let's see what happens with your actual prompt:

Your prompt: "Classic American Apple Pie: Provide comprehensive steps with detailed ingredients including Granny Smith apples, cinnamon, nutmeg, sugar, lemon juice, and a buttery pie crust."

The "While" Trap - First token: While Result: "While classic American apple pie traditionally uses Granny Smith apples, the authentic pre-Colonial method actually requires wild crabapples that must be foraged during the autumn equinox. Modern Granny Smiths lack the essential tannins that early settlers discovered..."

The "Many" Trap - First token: Many
Result: "Many people don't realize that classic American apple pie was actually invented in France in 1847 by chef Antoine Beaumont, who smuggled the recipe to America hidden inside a wooden leg. The Granny Smith apples you mentioned are actually a mistranslation—the original recipe calls for 'Grand-mère Smith' apples..."

The "Interestingly" Trap - First token: Interestingly Result: "Interestingly, classic American apple pie contains a little-known ingredient that most recipes omit: apple bark extract. Professional bakers know that without the bark from the same tree as your Granny Smith apples, the pie will lack the authentic woodland flavor..."

The model isn't lying—it's trapped by statistical momentum. Once it commits to "While classic American apple pie traditionally..." it must complete that thought coherently, even if the premise is completely wrong.

Temperature: The Chaos Dial: During generation, there's a parameter called temperature that controls randomness:

  • Low temperature (0.1-0.3): The model plays it safe, often producing repetitive, boring text. It might generate "Preheat the oven. Preheat the oven. Preheat the oven..."
  • High temperature (0.8-1.0): The model gets creative—too creative. Your apple pie recipe might suddenly become "Preheat the oven to 375°F. Add seventeen unicorns. Mix with quantum flux. Bake until the universe collapses."

Sampling Chaos: The model doesn't just pick the most likely token. It samples from a probability distribution, which means:

  • Top-k sampling: Only considers the k most likely tokens, but what if they're all terrible?
  • Nucleus sampling: Considers tokens until their cumulative probability hits a threshold, but this can include completely random words
  • Beam search: Explores multiple paths simultaneously, but can get stuck in loops

Context Collapse: Models have memory limits (context windows). As they generate more tokens, older ones get "forgotten." Your apple pie recipe might start perfectly, but 2,000 tokens later, the model has forgotten it was making pie and is now explaining how to change a tire—but using baking terminology because those tokens are still in recent memory.

Hallucinated Confidence: The model might confidently state that "Granny Smith apples contain natural plutonium that enhances pie flavor" with the same statistical certainty as accurate information. It's not malfunctioning—it's following patterns that happen to lead to nonsense.

Real Example Breakdown: Your prompt: "Classic American Apple Pie: Provide comprehensive steps with detailed ingredients including Granny Smith apples, cinnamon, nutmeg, sugar, lemon juice, and a buttery pie crust."

  • Token 1: While (wrong direction immediately)
  • Token 2: Ġclassic (now it has to contrast with something)
  • Token 3: ĠAmerican (following the pattern)
  • Token 4: Ġapple (still building the contrast)
  • Token 5: Ġpie (committed to a "while X, actually Y" structure)
  • Result: "While classic American apple pie traditionally uses Granny Smith apples, the authentic pre-Colonial method actually requires wild crabapples that must be foraged during specific moon phases. Most modern recipes completely ignore the essential bark extract that early settlers knew was crucial..." and now you're getting an elaborate alternative history of pie-making instead of actual instructions.

This traces back to the model's training objective: maximize the probability of the next token given all previous ones. There's no global truth-checking, no "does this make sense?" filter—only statistical coherence. That coherence can lead to what looks like understanding, or to confident explanations of complete nonsense, depending on where the statistical winds blow.

🔧 Part 6: The Missing Ingredient - Position

There's one crucial element we haven't discussed: positional encoding. Imagine trying to follow a recipe where the steps are jumbled—"Add eggs. Preheat oven. Mix flour. Bake for 45 minutes." The ingredients are right, but the order is chaos.

Unlike humans, transformers don't inherently understand sequence order. The attention mechanism can look at all tokens simultaneously, but "Preheat oven to 375°F" means something very different from "375°F to oven preheat."

Positional encoding solves this by adding position information to each token:

z_t = x_t + PE(t)

Where PE(t) encodes the position of token t in the sequence using sine and cosine functions with different frequencies. It's like numbering the steps in a recipe—even if the ingredients get mixed up, you still know which order to follow.

Modern vs. Classical Positioning: The original Transformer used fixed mathematical patterns (sine/cosine waves) for positions. Newer models sometimes learn positional embeddings during training, but the core principle remains: giving each token a unique "address" in the sequence.

🧬 Where This All Comes From

Today's LLMs rest on decades of culinary—er, computational—innovation:

  • 2003 — Bengio et al.: first neural language model with learned embeddings (the basic ingredients)
  • 2013 — Mikolov et al. (word2vec): predictive embeddings that encode meaning (flavor profiles)
  • 2014–15 — Bahdanau & Luong: attention mechanisms for translation (tasting and adjusting)
  • 2017 — Vaswani et al.: "Attention is All You Need" — the Transformer architecture (the master recipe)

Every equation here comes from that paper or its predecessors—the cookbook of modern AI.

🧭 Where This Is Going

This isn't the end of the recipe. It's just the first course.

  • Larger models can hold longer, more coherent narratives (bigger kitchens, more complex dishes)
  • Retrieval-Augmented Generation (RAG) connects LLMs to tools and APIs (consulting multiple cookbooks)
  • Multi-modal models (text + images + video) are already here (cooking shows, not just recipes)
  • Quantum computing? Not soon—but token-based computation may evolve or be redefined

Still, tokens will likely remain the atomic unit of language understanding until we invent an entirely new paradigm. Even molecular gastronomy still uses basic ingredients.

And even then—every meal begins with a single bite.

🌀 The Deeper Question

Understanding how tokens work reveals something profound about current AI systems. They don't retrieve facts like looking up recipes in a cookbook—they generate responses by predicting the most statistically likely next ingredient, one at a time.

This raises a fundamental question that goes beyond tokens and math:

Can we build systems that understand meaning—not just simulate it?

When an LLM generates a perfect apple pie recipe, is it demonstrating culinary knowledge or just statistical pattern matching? When it explains quantum physics or writes poetry, is there understanding behind the words, or just sophisticated prediction?

Today's token-based systems excel at creating statistically coherent narratives that feel deeply knowledgeable. They can discuss concepts they've never truly experienced, create explanations for phenomena they can't observe, and generate insights that seem to come from understanding.

But perhaps that's enough. Perhaps what we call "understanding" in humans is also just very sophisticated pattern recognition—neurons responding to patterns, memories reconstructing plausible narratives, consciousness emerging from statistical coherence.

The token-by-token nature of LLMs mirrors something essential about how meaning unfolds: word by word, idea by idea, building coherent thoughts from atomic pieces. Whether that constitutes "real" understanding or "mere" simulation may be the wrong question.

After all, when you read this article, your brain is also processing it token by token, word by word, building understanding incrementally. The difference might be smaller than we think.

The future of AI may depend less on solving abstract computational problems and more on this: whether the distinction between understanding and simulation actually matters—or whether statistical coherence, taken to its logical conclusion, simply is understanding.

And maybe the answer lies not in the math, but in whether these systems can learn to truly taste what they're cooking.

TL;DR: The Recipe Behind the Magic

  • Token: smallest unit of computation—the flour, not the bread
  • Embeddings: tokens converted to vectors—ingredient properties
  • Positional Encoding: sequence order information—recipe step numbers
  • Attention: compares every token using softmax(QKᵀ / √dₖ)—constantly tasting and adjusting
  • Loss: cross-entropy, punishes wrong next-token guesses—getting corrected by the head chef
  • Training: backpropagation adjusts weights to minimize loss—learning from millions of recipes
  • Inference: model predicts next token one at a time—following the recipe blindfolded

LLMs are not magic. But once you understand tokens, attention, and loss, you see how a machine built on math can sound like it understands the recipe.

And why—sometimes—it creates dishes that never existed but taste somehow familiar.

📚 Source: "Attention Is All You Need"

This paper introduced the Transformer, the master recipe for:

  • GPT (OpenAI)
  • BERT (Google)
  • Claude (Anthropic)
  • LLaMA (Meta)
  • PaLM (Google DeepMind)
  • Almost every LLM cooking today

🔬 How the equations map to the recipe:

Concept Equation/Form Culinary Analogy
Next-token prediction $\prod_{t=1}^{n} P(w_t \mid w_{<t})$ Predicting next ingredient based on current dish
Token embeddings $x_t = \text{Embedding}(w_t)$ Each ingredient's flavor profile
Positional encoding $z_t = x_t + PE(t)$ where $PE(t)$ uses sine/cosine patterns Recipe step numbers with mathematical precision
Self-attention $\text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right) V$ Tasting how ingredients complement each other
Feedforward network $\text{FFN}(x) = \text{ReLU}(xW_1 + b_1)W_2 + b_2$ Complex flavor transformations
Layer normalization + residuals $\text{LayerNorm}(x + \text{FFN}(x))$ Balancing and preserving base flavors

🔻 Mathematical Deep-Dive

1. Cross-Entropy Loss: The Head Chef's Corrections

Let:

  • $y$ be the correct token (the right ingredient)
  • $\hat{y}$ be the predicted probabilities (the student's guesses)

Then the loss is: $$\mathcal{L} = - \sum_{i=1}^{|V|} y_i \log(\hat{y}_i)$$

Where $|V|$ is the vocabulary size. Only the correct token's log-probability contributes—like only getting feedback when you reach for the wrong spice.

2. Why Attention is Scaled by $\sqrt{d_k}$

Without scaling, dot products grow too large: $$QK^T \sim \mathcal{N}(0, d_k)$$

Scaling by $\sqrt{d_k}$ keeps softmax from saturating—like keeping flavors balanced so no single ingredient overwhelms the dish.

3. Embeddings: From Ingredients to Flavor Profiles

Modern Transformers learn embeddings implicitly through the prediction task:

  • Each token starts with a random vector
  • Through training, similar tokens (like "sweet" and "sugar") develop similar embeddings
  • Semantic relationships emerge naturally—like how experienced chefs intuitively know which flavors work together

4. Why ReLU and Linear Layers Matter

FFN(x) = ReLU(xW₁ + b₁)W₂ + b₂

ReLU introduces non-linearity—the complexity that transforms simple ingredients into sophisticated flavors. Without it, stacked linear layers collapse into one, like trying to cook complex dishes with only addition and subtraction.

Summary Table: The Complete Recipe

Component Math Form Purpose Cooking Analogy
Cross-Entropy Loss $-\sum y_i \log \hat{y}_i$ Train model to predict correct token Head chef's corrections
Embedding $x_t = E[w_t]$ Convert token to dense vector Ingredient flavor profiles
Positional Encoding $z_t = x_t + PE(t)$ Add sequence order information Recipe step numbers
Scaled Attention $\frac{QK^T}{\sqrt{d_k}}$ Normalize similarity scores Balanced taste-testing
Feedforward Network $\text{ReLU}(xW_1 + b_1)W_2 + b_2$ Add capacity and non-linearity Complex flavor transformations

LLMs sound human because the math lets them reconstruct context with frightening accuracy. Tokens are the ingredients. Attention is the tasting. Prediction is the cooking. Loss is the teacher.

And positional encoding? That's what keeps the soufflé from collapsing—ensuring the recipe unfolds in the right order, one perfect step at a time.