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Artificial intelligence has made great strides since the deep learningrevolution, but AI systems still struggle to extrapolate outside of theirtraining data and adapt to new situations. For inspiration we look to thedomain of science, where scientists have been able to develop theories whichshow remarkable ability to extrapolate and sometimes predict the existence ofphenomena which have never been observed before. According to David Deutsch,this type of extrapolation, which he calls "reach", is due to scientifictheories being hard to vary. In this work we investigate Deutsch's hard-to-varyprinciple and how it relates to more formalized principles in deep learningsuch as the bias-variance trade-off and Occam's razor. We distinguish internalvariability, how much a model/theory can be varied internally while stillyielding the same predictions, with external variability, which is how much amodel must be varied to accurately predict new, out-of-distribution data. Wediscuss how to measure internal variability using the size of the Rashomon setand how to measure external variability using Kolmogorov complexity. We explorewhat role hard-to-vary explanations play in intelligence by looking at thehuman brain and distinguish two learning systems in the brain. The first systemoperates similar to deep learning and likely underlies most of perception andmotor control while the second is a more creative system capable of generatinghard-to-vary explanations of the world. We argue that figuring out howreplicate this second system, which is capable of generating hard-to-varyexplanations, is a key challenge which needs to be solved in order to realizeartificial general intelligence. We make contact with the framework ofPopperian epistemology which rejects induction and asserts that knowledgegeneration is an evolutionary process which proceeds through conjecture andrefutation.

Applying Deutsch's concept of good explanations to artificial intelligence and neuroscience -- an initial exploration