Here’s a metaphor/framework I’ve found useful but am trying to refine, so feedback welcome. Visualize the deforming rubber sheet model commonly used to depict masses distorting spacetime. Your goal is to roll a ball onto the sheet from one side such that it rolls into a stable or slowly decaying orbit of a specific mass. You begin aiming for a mass on the outer perimeter of the sheet. But with each roll, you must aim for a mass further toward the center. The longer you roll, the more masses sit between you and your goal, to be rolled past or slingshot-ed around. As soon as you fail to hit a goal, you lose. But you can continue to play indefinitely. The model’s latent space is the sheet. The prompt is your rolling of the ball. The response is the path the ball takes. And the good (useful, correct, original, whatever your goal was) response is the orbit of the mass you’re aiming for. As the context window grows, there are more pitfalls the model can fall into. Until you lose, there’s a phase transition, and the model starts going way off the rails. This phase transition was formalized mathematically in this paper from August. The masses are attractors that have been studied at different levels of abstraction. And the metaphor/framework seems to work at different levels as well, as if the deformed rubber sheet is a fractal with self-similarity across scale. One level up: the sheet becomes the trained alignment, the masses become potential roles the LLM can play, and the rolled ball is the RLHF or fine-tuning. So we see the same kind of phase transition in both prompting (from useful to hallucinatory) and in training. Two levels down: the sheet becomes the neuron architecture, the masses become potential next words, and the rolled ball is the transformer process. In reality, the rubber sheet has like 40,000 dimensions, and I’m sure a ton is lost in the reduction.