Instruction tuned LLaMA 65B/Falcon 40B are good, especially with an embeddings database.
...But OpenAI has all the name recognition and ease of use now, so it might not even matter if others ambiguously surpass OpenAI models.
It's $20 a month and comes with 300 GPT-4 messages and 1000 Claude 1.2 messages.
By comparison, ChatGPT Plus gives gives you up to 6000 GPT-4 messages a month for the same price (admittedly it would be hard to use that many as they are given in 3 hour blocks).
In a nutshell, part of your llm prompt (usually your most recent question?) gets fed as a query for the embedding/vector database. It retrieves the most "similar" entries to your question (which is what an embedding database does), and that information is pasted into the context of the llm. Its kinda like pasting the first entry from a local Google search into the beginning of your question as "background."
Some implementations insert your old conversations (that are too big to fit into the llm's context window) into the database as they are pushed out.
This is what I have seen, anyway. Maybe some other implementations do things better.
How is it embedded? Using a separere embedding model, like Bert or something? Or do you use the LLM itself somehow? Also, how do you create content for the vector database keys themselves? Also just some arbitrary off the shelf embedding? Or do you train it as part of training the LLM?
You do not need a fancy cloud hosted service to use an embeddings database like you do not need one to use a regular databse (although you could).
Check https://github.com/kagisearch/vectordb for a simple implementation of a vector search database that uses local, on-premise open source tools and lets you use an embeddings database in 3 lines of code.