Prompt: Word2Vec and the Geometry of Meaning
The prompt that generated Chapter 1 — embeddings, cosine similarity, and why dense vectors beat one-hot encoding.
Write a markdown chapter for a book to help the reader learn and understand the math behind wordVec and other token embeddings that are used as embedding layers for LLMs. In terms of style, Start with (simplified) historical anecdote of maybe the inventor tackling some problem not solved with the methods used before, laying the context behind this problem as an example both in concrete specfic number values and python code and in terms of looking at motivation, human stakes, tracing the author thinking of pursuing one idea, then seeing it’s a deadend and moving to the next one and so on. Basically this chapter should work for someone who is trying to grok the intuition behind the algorithms to get intuition on mathematical arguments on what mathematical properties of using the floating point vectors in particular is the right tool for the job. Maybe then the chapter should dig deep into the arguments that stem from basic linear algebra and properties of geometry of high-dimensional vector spaces vs 1D, 2D, 3D vector spaces and so on.