Vector Database by Hand: A 10-Step Walkthrough of RAG Mechanics
ProfTomYeh · x · 2026-08-27
A hands-on tutorial explaining the underlying principles of Vector Databases using manual calculation, covering the core steps in Retrieval Augmented Generation (RAG).
Core Workflow (10 Steps):
- Given Data: A dataset of three sentences.
- Word Embeddings: Looking up vector representations for each word.
- Encoding: Processing sequences via a linear layer and ReLU (representing a Transformer).
- Mean Pooling: Averaging word vectors to get sentence embeddings.
- Indexing: Multiplying by a projection matrix to reduce dimensions for storage.
6-7. Data Processing: Repeating steps to index other sentences in the database.
- Query Processing: Mapping the query through the same pipeline into the vector space.
- Dot Products: Calculating dot products between the query and stored vectors to estimate similarity.
- Nearest Neighbour: Scanning for the maximum dot product to find the answer. Real-world databases use approximate nearest neighbor indexes like HNSW to optimize this.
Takeaway: A vector database is essentially an embedding pipeline, a projection, and a dot product.
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