If I were to sell the power of LLMs as powerful research agents, and if I had enough money, I could think about introducing little "gems" into the training set of LLM so that my model would be able to discover new theorems and proofs. There is a lot of money at the table, and I am sure there are a lot of genius people with little pay. Perhaps this kind of thinking is wrong?, only bad people would think like this?, how could one detect such a trick without knowing the training set?
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