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I had an idea when reading it that I think is pretty interesting. You mention that both the grokking of a small amount of data repeated many times, and models trained on a great deal of data are highly general. Repeated data during training is also mentioned as a significant negative for large models. These are very much in tension.

My idea is this. Split the training data into two parts, one vastly larger than the other. First, train a model on a small amount of data many times in a way designed to make it grok the task, such as weight decay. Second, train it on the rest of the very large amount of data. Third, compare it to the a model trained on both parts without repeats. See how they compare. (I don't know if people have done this. I'm definitely a layman when it comes to such things.)

Models are often 'fine-tuned' on things later. You could see this as sort of the opposite, where we tune it for the task first, and then train it.