  We address the main problem of self-learning LLM: the question of what to
learn. We propose a self-learning LLM framework that enables an LLM to
independently learn previously unknown knowledge through selfassessment of
their own hallucinations. Using the hallucination score, we introduce a new
concept of Points in the Unknown (PiUs), along with one extrinsic and three
intrinsic methods for automatic PiUs identification. It facilitates the
creation of a self-learning loop that focuses exclusively on the knowledge gap
in Points in the Unknown, resulting in a reduced hallucination score. We also
developed evaluation metrics for gauging an LLM's self-learning capability. Our
experiments revealed that 7B-Mistral models that have been finetuned or aligned
and RWKV5-Eagle are capable of self-learning considerably well. Our
self-learning concept allows more efficient LLM updates and opens new
perspectives for knowledge exchange. It may also increase public trust in AI.
