Explanation

Prompt

Give me a comprehensive, technically detailed explanation of tokenization and embeddings in large language models (LLMs). Assume I’m willing to learn the technical concepts, but define unfamiliar terms as you introduce them. Organize the explanation into these sections: Tokenization: What tokens are; how text is converted into token IDs; how common approaches such as byte-pair encoding (BPE), WordPiece, and byte-level tokenization work; and how tokenizers handle punctuation, whitespace, numbers, rare words, and multilingual text. A worked example: Take one sentence and show how it might be split into tokens and mapped to IDs. Explain why the exact result depends on the tokenizer. Embeddings: Explain embedding vectors, how token IDs are mapped to vectors, what vector dimensions represent, and how learned token embeddings differ from contextual representations produced later in the model. How they work together: Trace text from input tokens through embeddings and a Transformer, including positional information and how token representations change across layers. Training: Explain how tokenizers are created, how embedding parameters are learned, and how next-token prediction shapes the model’s representations. Practical implications: Discuss vocabulary size, sequence length, token limits, out-of-vocabulary handling, multilingual efficiency, and why token counts can differ from word counts. Distinguish general principles from implementation choices that vary between models. Include equations or small pseudocode examples where useful, and end with a glossary and a concise end-to-end summary.