Overtraining has actually shown to result in emergent math behavior (in multiple independent studies), so that is no longer true. The studies were done where the input math samples are “poisoned” with incorrect answers to example math questions. Initially the LLM responds with incorrect answers, then when overtrained it finally “figures out” the underlying math and is able to solve the problems, even for the poisoned questions.
Overtraining has actually shown to result in emergent math behavior (in multiple independent studies), so that is no longer true. The studies were done where the input math samples are “poisoned” with incorrect answers to example math questions. Initially the LLM responds with incorrect answers, then when overtrained it finally “figures out” the underlying math and is able to solve the problems, even for the poisoned questions.