A model compresses a state space by capturing a set of invariances that predict the variance in the states. Its free parameters define the latent space of the model and should ideally fully correspond to the variability, the not-invariant (= unexplained) remainder of the state.
An invarance is an aspect of the data that does not change. For instance, all even numbers have in common that their lowest bit is 0. All Russian words have in common that none contains an h. All cells contain carbon.
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(HI!) This is cool to ponder! The way that invariances relate to reasoning still eludes me... (and seems important wrt ground truth) E.g how can I think about the 'reasons' cell contain carbon so to 'make this invariance conditional on its semantics' (a phrase I don't quite get!)
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“contains” is a transitive part-of relationship. Specifically, it can be defined as the transitive hull of the relationship of a set to a true sub-set. You can use that to compute what Aristotle called the causa materialis.
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