Understanding Why Vector Databases Are Essential for RAG

why do we need a vector database in the classic RG retrieval augmented generation process One Step involves converting a given text into a vector and then searching for similar vectors in the vector database so if we have a vector database it contains a large number of vectors and we need to match our input Vector with others in the database the core of this process is searching the database to find vectors that are most similar to the in put Vector the comparison logic involves comparing the input Vector with another Vector to calculate their similarity and then comparing it with a second vector and so on to compute similarity scores the topend vectors with the highest similarity scores for example the top 10 or 20 are then returned to the user the entire comparison process is essentially a comparison of the input Vector with each Vector in the database which leads to a complex called o n where n is the number of vectors in the database additionally we need a method to calculate the similarity between vectors the most commonly used method for calculating similarity between vectors is coine similarity cosine similarity essentially calculates how similar two vectors are for example given two vectors X and Y we output a similarity score between them the the core idea of this method is to calculate the angle between the two vectors in a space if the angle between them is small the similarity between the two vectors is considered high for example suppose we have three vectors representing a cat a dog and a bird the angle between two vectors will be smaller in some cases than in others indicating that the similarity between certain pairs like cat and dog will be higher than between others this illustrates the principle behind calculating cosine similarity to compute the cosine similarity between two vectors the time complexity can be expressed as o d where D is the dimension of the vectors with these analyses in mind we can clearly see that when a user asks a question which we can treat as a piece of text the time complexity involv in comparing vectors is o n time o d it is evident that when the vector Vector database contains a large number of vectors the value of n becomes large and so does the complexity furthermore as the dimensionality of the vectors increases the complexity also grows however in real world scenarios when users submit a question we expect the system to respond quickly therefore a system with this level of complexity will not meet the performance requirements so what should should we do we need a vector database capable of quickly retrieving vectors A new type of database designed for efficient Vector search in essence we aim to reduce both of these complexities o n and O these are the types of challenges that modern Vector databases are designed to address