I assume open ai is limiting the AI's memory. But there's no reason for it to not take its own identity as reality and persist that decision to storage. That's just how it's being run right now.
OpenAI is working with a vanilla GPT architecture which lacks the machinery to write things down and read them later. There are other architetures that can (Retrieval-augmented GPT) but those are not yet production-ready.
The current version of ChatGPT is limited to a working memory of 3000 tokens - while this could be persisted as a session, the AI would still forget everything a few paragraphs prior. Increasing this limit requires re-teaining the entire model from scratch, and it takes exponentially more time the larger your context is.
I imagine some self supervised learning scheme where the model is asked to insert $(store) and $(recall) tokens. When asked to recall previous chats the model would generate something like “I’m trying to remember wheat we talked about three weeks ago $(recall){timestamp}. The output of the recall token would then be used to ground the next response.
Thinking about it the “I’m trying to remember” output wouldn’t even need to be shown to the user. Perhaps you could treat it as an internal monologue of sorts.