For example, deep learning and various clustering algorithms allow us to figure out whether the data had any sorts of non-temporal regularities. ... That doesn't seem to be equivalent to considering infinitely many hypotheses.
I think it's useful to think of the parameter-space for your model as the hypothesis-space. Saying "our parameter-space is R^600" instead of "our parameter-space is all possible algorithms" is way more reasonable and computable, but what it would mean for an unsupervised learning algorithm to have no hypotheses would be that it has no parameters (which would be worthless!). Remember that we need to seed our neural nets with random parameters so that different parts develop differently, and our clustering algorithms need to be seeded with different cluster centers.
Does it mean then that neural networks start with a completely crazy model of the real world, and slowly modify this model to better fit the data, as opposed to jumping between model sets that fit the data perfectly, as Solomonoff induction does?
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