I feel like extensive pretraining goes against the spirit of generality.
If you can create a general machine that can take 3 examples and synthesize a program that predicts the 4th, you've just solved oracle synthesis. If you train a network on all human knowledge, including puzzle making, and then fine-tune it on 99% of the dataset and give it a dozen attempts for the last 1%, you've just made an expensive compressor for test-maker's psychology.
If you can create a general machine that can take 3 examples and synthesize a program that predicts the 4th, you've just solved oracle synthesis. If you train a network on all human knowledge, including puzzle making, and then fine-tune it on 99% of the dataset and give it a dozen attempts for the last 1%, you've just made an expensive compressor for test-maker's psychology.