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.
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The proper representation of invariances (which include allowed set of values of the free parameters) is conditional on the reason for an invariance. The relationship to this reason is itself an invariance that needs to be made conditional on the foundations of its semantics.
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Replying to @Plinz
Ok, I'm not smart enough for this thread, but I want to understand! Could you give an example? Sorry if this is a dumb request.
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Replying to @mattgiammarino
Discovered Invariance in the data = structure of the model (a set of variables with value ranges and a set of computational relationships between them) Discovered Variance in the data = the set of values of the variables that will explain most of the observations I am making
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The computational relationships will have to be defined, too, which means that we must construct models that can reproduce them, from other models that ultimately bottom out in a set of elementary automata.
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