Introducing LLms

Text Tokenization and Embeddings in Deep Learning Why Text Needs to Be Numbered Deep learning models are based on processing numbers Language models are built on mathematics, and math is based on numbers Optimization, learning algorithms, and probabilities all require numerical representations Text must be represented as numbers for computational processing What is a Token? A token is a piece of text that can be represented as an integer. Examples of Tokenization: Character-level: The word "HELLO" represented as five numbers (a vector with one number for each character) Subword-level: "HELLO" split as "HE-LLO" → two numbers representing two subwords Word-level: The entire word "HELLO" as a single token (one number) Why Not Use Characters as Tokens? Simple character mapping (e.g., a→1, b→2, ... z→26) has several problems: Problem 1: Unicode Complexity Many different unicode systems exist for letters across languages Problem 2: Statistical Inefficiency Ignores statistical regularities in language Misses patterns and relationships between character sequences Problem 3: Memory Limitations Requires significant additional memory Severely limits the context window size How LLMs Actually Work Important: LLMs don't work directly with tokens - they work with embeddings! The Processing Pipeline: Text → Token ID → Embedding → [LLM Processing] → Unembedding → Token → Text Text is converted into tokens Tokens must be converted into embeddings before the LLM can process them LLMs modify embeddings for classification and generation tasks It's all about the embeddings What Are Embeddings? Embeddings are dense numeric representations of tokens. Advantages Over Simple Integers: Efficiency: More text can be represented using fewer numbers Semantic Relations: Relationships across tokens can be represented Characteristics of Real Embeddings: High-dimensional: Often more than 1000 dimensions Not human-interpretable: Abstract mathematical representations Dynamic: Modified during model calculations (e.g., the "dog" vector can change based on context) Tokenization Challenges Finding the optimal tokenization strategy is difficult: Trade-offs: Fewer tokens: ✓ Less memory usage ✓ Improved generalization ✗ Less efficient and effective More tokens: ✓ Better text compression ✓ Can convey more information ✗ Requires more training Key Considerations: Statistical dependencies change across languages Dependencies vary between databases within the same language Tokenization must be learned from text Different texts will create different tokenization schemes Key Definitions Encoder: A function that maps text into integers Decoder: The opposite of encoder - a function (lookup table) that maps integers back into text Inverse Property: decoder(encoder(x)) = x Summary Text must be transformed into numbers before LLM processing A chunk of text (token) can be a character, subword, or full word Embeddings are dense representations of tokens Both tokenization and embeddings are learned from data There are many valid ways to create these schemes This is an excellent overview of tokenization and embeddings! You've covered the fundamental concepts clearly. Let me add a few insights that might complement your notes: Additional Context on Tokenization Methods Byte-Pair Encoding (BPE) is one of the most common tokenization algorithms used today (GPT models, for instance). It starts with characters and iteratively merges the most frequent pairs to create subword tokens. This helps balance vocabulary size with semantic meaningfulness. WordPiece (used by BERT) and SentencePiece (used by T5, LLaMA) are other popular approaches that achieve similar goals through slightly different algorithms. The Embedding Space Your point about embeddings capturing semantic relations is crucial. In practice, this means: Similar words cluster together in the embedding space Vector arithmetic can capture relationships (the classic example: king - man + woman ≈ queen) Contextualized embeddings (from transformers) can represent the same word differently based on surrounding context Practical Trade-offs The tokenization choice significantly impacts: Computational efficiency: Fewer tokens = faster processing Multilingual capability: Byte-level tokenization handles any language but needs more tokens Out-of-vocabulary handling: Subword tokenization can handle novel words by breaking them into known pieces A Concrete Example For the sentence "The tokenization is interesting": Character-level: ~30 tokens (including spaces) Subword (BPE): ~6-8 tokens (might split "tokenization" into "token" + "ization") Word-level: 4 tokens Each approach affects how much context fits in the model's window and how well it generalizes.