The problem with LLMs is that the output is inherently stochastic - i.e there isn't a "I don't have enough information" option. This is due to the fact that LLMs are basically just giant look up maps with interpolation.
Energy minimization is more of an abstract approach to where you can use architectures that don't rely on things like differentiability. True AI won't be solely feedforward architectures like current LLMs. To give an answer, they will basically determine alogrithm on the fly that includes computation and search. To learn that algorithm (or algorithm parameters), at training time, you need something that doesn't rely on continuous values, but still converges to the right answer. So instead you assign a fitness score, like memory use or compute cycles, and differentiate based on that. This is basically how search works with genetic algorithms or PSO.