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.
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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Thank you! That is very helpful. I'm going to chew on it for a bit to ensure my follow up is cogent....
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Let me see if I can come up with an example. You make an invariant map of your body surface by counting how often sensory nerves fire simultaneously: these will often be neighbors. Then you can infer when objects are moving over your skin, and reduce the firing of nerves to that.
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The part of the variance in the data that I cannot explain is called noise. The part of the invariance that I have not found is called uncertainty.
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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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