Vector

Vectors are fundamental building blocks in both mathematics and machine learning.

The word "vector" traces its roots to the Latin, meaning "carrier" or "one who carries." This original sense evoked an entity that transports or conveys something from one point to another. In modern data science and machine learning, vectors have maintained this essence of directionality and transportation, albeit in a more abstract mathematical context.

In today's world of language models and data, vectors are like lists that hold related numbers or information in a specific order. Think of them as organized containers for data. These containers are crucial because they help describe linguistic features, store information, and put data in a format that language models can easily work with.

Just as the original Latin word suggested movement, vectors in language models facilitate navigation through the vast expanse of textual data, but they do so in a way that's far more intricate than a simple map. Instead of mere arrows pointing the way, imagine vectors as multi-dimensional constellations, each star representing a word or concept. The distances and relationships between these stars encode the rich context and meaning woven into language.

Vectorization

Vectorization is the crucial process of transforming tokenized text into numerical representations, making it suitable for processing by language models. Once text is broken down into tokens (individual words or subwords), vectorization assigns each token a unique numerical vector.

These vectors are designed to capture not only the literal meaning of the tokens but also their nuanced semantic connotations and relationships within the surrounding context. This is achieved through various techniques such as word embeddings (e.g., Word2Vec, GloVe, FastText) that map words into a continuous vector space where semantically similar words are positioned closer together.

Vectorization is akin to how cartographers translate the physical world into maps; it translates language into a numerical landscape that machines can navigate. In applications like chatbots, vectorization enables these systems to "understand" user input and generate contextually relevant responses. During inference, the vectorized representations of input tokens allow language models to produce coherent and contextually appropriate text.

Advanced techniques, such as Retrieval-Augmented Generation (RAG), further enhance this process by allowing models to retrieve and incorporate information from external sources. This ensures that generated responses are both informed and accurate, leveraging external knowledge bases to supplement the model's understanding.

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