1. Context Window: The Model's Working Memory

Concept: The context window is the model's "working memory"—the total number of tokens (chunks of text) it can consider at once. This includes both your input and the model's output.
Modern AI models, known as transformers (introduced by Google), use an attention mechanism to focus on all tokens in this window simultaneously—but nothing outside it.

Everyday Example: Imagine a whiteboard with limited space. You write your question (input tokens) and leave room for the model's answer (output tokens). If your question fills the board, there's less space for the answer. If you run out of space, the model stops writing—even mid-sentence.

Why it matters:

• Hard limit: input tokens + output tokens ≤ max context window
• If your input is large, you have less room for the model's answer.
• If you hit the limit, the model will stop—sometimes in the middle of a sentence.
• This applies to all transformer models: OpenAI's GPT-4o/o1, Anthropic's Claude 3.7, and Amazon's Nova Premier.
• Cost control: Although foundational models have a maximum context window, most APIs let you set a smaller limit (using parameters like max_tokens) if you want to control costs or keep responses shorter.

2. Tokenization: Breaking Down Text

Concept: Tokenization splits text into small pieces called tokens that the model can process within its context window.

Everyday Example: Think of tokenization like cutting a pizza. The whole pizza is your full text, and the slices are your tokens.

Practical Application: Quick Token & Cost Estimation for Developers:
For English, on average, 1 token ≈ 4 characters (including spaces and punctuation) or ¾ of a word.
Reference: OpenAI Tokenizer

How to use:

• Count words or characters in your input and expected output.
• Estimate tokens (words × 1.33 or characters ÷ 4).
• Add input and output tokens for total usage.
• Check your provider's pricing—most charge less for input tokens and more for output tokens.
• Multiply by the respective rates to estimate total cost.

3. Embeddings: Understanding Meaning

Concept: Embeddings are numerical representations of tokens that capture their meaning in a mathematical space.

Everyday Example: Imagine a map where similar words are clustered together. "Happy" and "joyful" would be neighbors, while "happy" and "sad" would be far apart.

Practical Application: Embeddings allow models to understand semantic relationships and make connections between concepts that weren't explicitly mentioned.

4. Logits: Making Predictions

Concept: Logits are raw numerical scores the model assigns to each possible next token before making its final selection.

First phase: The model splits the prompt into tokens, converts the tokens to embeddings, and processes the sequence of embeddings through its layers (e.g., transformer blocks), which use attention mechanisms to understand relationships and context. The model then produces logits—raw scores for every possible next token. These logits are converted to probabilities using the softmax function (see Wikipedia). This calculation phase is deterministic—identical inputs always produce the same probability distribution.

Second phase: The model selects tokens from this distribution, either deterministically (by always choosing the highest-probability token, if configured to do so) or with controlled randomness (to balance accuracy with creativity, depending on the sampling parameters).

Everyday Example: When completing "The capital of France is ____," a model assigns high scores to relevant answers like "Paris" and low scores to irrelevant options like "banana."

Practical Application: The temperature, topP, and topK parameters control creativity vs. predictability in responses. These parameters let you balance deterministic, factual outputs with more creative, varied responses.

5. Response and Structured Output

Concept: Models can format outputs as either free-form text or structured data (JSON, XML, etc.).

Everyday Example: Compare asking for weather information as a casual description versus a formatted weather report with specific fields.

Practical Application: Structured outputs are essential when the AI's response needs to be processed by other systems rather than read by humans.

6. LLM Evolution & Architectural Advances

Early LLM Development (2017-2022)

The modern Large Language Model era began with the 2017 paper "Attention Is All You Need," which introduced the Transformer architecture. This revolutionary approach replaced recurrent neural networks with three key innovations:

• Self-attention mechanism: Allowing models to connect related words regardless of distance
• Parallel processing: Enabling simultaneous rather than sequential computation
• Flexible architecture: Supporting various NLP tasks through encoder-decoder components

Following this breakthrough, researchers discovered the "scaling law" phenomenon: model capabilities improve predictably as parameters, training data, and computing power increase. This insight led to a rapid expansion in model size:

The scaling era culminated with the release of ChatGPT on November 30, 2022, which brought LLMs into mainstream use through its user-friendly interface and impressive capabilities.

The Rise of Reasoning Models (2023-Present)

Around 2023, a new generation of models emerged with enhanced reasoning abilities, representing a significant leap beyond simple pattern recognition. To build these reasoning models, training approaches evolved from basic transformer architectures to include explicit reasoning demonstrations, self-critique methods, and human feedback on multi-step solutions.

Note: When a model shows its reasoning, all reasoning steps count toward the context window limit and output token costs. Parameters like max_tokens and budget_tokens can control total output length and costs.

Current Limitations of LLMs

Despite impressive advances, even today's most sophisticated models face significant challenges:

• Struggle with complex multi-step reasoning (e.g., solving novel mathematical proofs or multi-constraint optimization problems)
• Difficulty with tasks requiring specialized domain knowledge (e.g., advanced legal reasoning or medical diagnosis)
• Inconsistent performance on spatial reasoning tasks (e.g., complex physical systems or 3D visualization problems)

Future Research Directions

The field is rapidly evolving beyond current LLM limitations, with several promising research directions that could transform how we build AI applications:

These research areas could address some of the current limitations of autonomous agents and reduce the engineering overhead for building systems that can work on complex tasks while interacting with both physical and digital worlds.