AI runs on math. Which creates an obvious problem: most of the things we want AI to understand — words, sentences, ideas, images, relationships between concepts — aren't numbers.
The solution is embeddings: a way of converting meaning into numbers, specifically into points in a high-dimensional mathematical space. Every word, sentence, or concept gets mapped to a location in that space, and the location isn't arbitrary. It's learned from patterns in data, and it captures something genuine about meaning.
Here's the part that makes this click. Words that mean similar things end up close together in the embedding space. "Doctor" and "physician" are neighbors. "Cat" and "kitten" are neighbors. "Paris" and "France" are close in the same way that "Berlin" and "Germany" are close. The relationships between concepts are encoded in the geometry. You can do arithmetic on meaning: the vector for "king" minus the vector for "man" plus the vector for "woman" lands very close to the vector for "queen." That's not a trick. It's what the model actually learned from reading enough text.
This is why embeddings were such a pivotal development in AI. Before them, the dominant approach was to treat words as discrete symbols with no inherent relationship to each other. "Cat" and "kitten" were just two different tokens; the model had no way to know they were related unless it was explicitly told. Embeddings gave models a way to represent the structure of meaning, not just the presence of words, and that made a whole class of tasks suddenly tractable: semantic search, translation, question answering, and eventually the large language models that power most of what you use today.
The articles ahead get into the specific types: embedding models, sentence embeddings, document embeddings, and the distinction between dense and sparse vectors. Each one is a variation on the same core idea, applied at a different granularity or for a different purpose.
