An Intro to Large Language Models and the Transformer Architecture: Talking to a calculator

Source: Dev.to

“All models are wrong, but some are useful.”
— George E. P. Box

Overview

Large language models (LLMs) are essentially structured sets of numerical parameters—often billions—organized into matrices and vectors that emerge from the training process. By exposing these models to enormous datasets, they learn statistical relationships between tokens and build an internal representation of language.

At a high level, an LLM functions as a sophisticated autocomplete: it predicts the next piece of text without genuine reasoning or understanding. The most capable models, able to tackle complex, PhD‑level mathematical tasks, contain tens or hundreds of billions of unquantized parameters, but their cost makes them impractical for broad use in the near future.

Transformer Architecture

The true engine of modern LLMs is the transformer architecture. Depending on the model family, transformers may use:

• Decoder‑only layers (e.g., GPT models)
• Encoder‑only layers
• Encoder–decoder stacks

For a deeper dive, see the article on Understanding Transformer Architecture.

Tokenization and Embeddings

Tokenization

Before text enters a model, it must be converted into a machine‑readable format. The text is split into tokens, which can represent characters, syllables, words, or subwords.

Among tokenization strategies, Byte‑Pair Encoding (BPE) and its modern variants are especially widespread due to their efficiency and strong performance in popular models.

Embedding

Each token is mapped to a continuous numerical vector through an embedding process. Embeddings place the model in a high‑dimensional space where patterns, relationships, and semantic meaning can be encoded. Tokens are processed both individually and collectively, generating dense vector representations that serve as the basis for all subsequent reasoning inside the model.

Unembedding (Output Projection)

After transformation, the refined vectors are passed through an unembedding (or output projection) layer, converting the internal numerical representation back into tokens that form the words and sentences of the model’s output.

Limitations and Hallucinations

LLMs do not understand the world as humans do, leading to hallucinations—outputs that are plausible but factually incorrect. Despite this, they can be useful in many contexts. As Professor Aleksander Mądry noted:

“AI is not just any technology; it is a technology that accelerates other technologies and science. It serves as a highway to faster progress. Ignoring it wouldn’t be wise.”

Understanding how LLMs and transformers work is essential for making informed decisions about when and how to use them effectively.

Quantization and Practical Use

Widely accessible models are often quantized, meaning they use reduced numerical precision to lower computational cost and make them more affordable. Quantization can affect performance: in practice, a GPT model may excel at softer self‑development tasks but struggle with tasks requiring detailed, domain‑specific knowledge, where it may fail to provide partial answers or be guided toward a complete solution.