Wow, very nice! First of all, I will preface by admitting that I have not worked with LLMs to the degree of making a toy implementation. Your explanation of the sampling techniques is insightful but doesn’t clear up my confusion. Why does sampling imply the absence of higher level structure in the model?
For example, even though poker is highly influenced by chance, I can still have a plan that will increase my likelihood of winning. I don’t know what card will be drawn next but I can prepare strategies for each possible card. I can have preferences for which cards I want to be drawn next.