Earlier quoted context omitted.
The goal isn't to be the best LLM, the goal is to be the first self-improving LLM. On paper, whoever gets there first, along with the needed compute to hand over to the AI, wins the race.
Self-improving LLM is as probable as a perpetual motion machine. Practically, LLMs train on data. Any output of an LLM is a derivative of the training data and can't teach it anything new. Conceptually, if a stupid AI can build a smart AI, it would mean that the stupid AI is actually smart, otherwise it wouldn't have been able too.
The fact is, there is no law of physics that prevents the existence of a system that can decrease its internal entropy (complexity) on its own, provided you constantly supply it with energy (negative entropy). Evolutionary algorithm (or "life") is an example of such a system. It is conceivable that there is a point when a LLM is smart enough to be useful for improving its own training data, which then can be used to train a slightly smarter version, which can be used to improve the data even more etc... Every time you inference to edit the training data and train, you are supplying a large amount of energy into the system (both inferencing and training consumes a lot of energy). This is where the decrease in entropy (increase in internal model complexity and intelligence) can come from.