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.
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 function that connects models of touching objects and the nerve firings should optimize for generating a possible world state for every configuration of free variables. If you add more modalities, such as sight, they need be compatible in this sense.
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This implies that if there is a mismatch between the object you infer by touch and the object you infer by sight, you will have to come up with a mechanism that explains that mismatch (such as a mirror).
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Thanks for teaching me! So is the (first) model a thing that outputs 'where is my body' based on inputs from the sensory system? Using some firing --> body location function?
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To know where your body is, you need a model of the whole world around it. You may start with the body surface as ground zero, then map it as a suitably deformed volume into a flat space, and then populate that space with other objects, before you make a global map of all objects
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I can't figure out what 'noise' and 'uncertainty' are . Maybe noise is sensory firing patterns that can't be translated into body locations (using the current function)? uncertainty would be patterns of nerve firing that create ambiguity in the body map? Corrections appreciated
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Noise is incompressible information, i.e. information that you cannot relate to other information, such as nerves randomly firing. Uncertainty is estimated difference between model and ground truth. This includes uncertainty about the model quality (i.e. the model of your model).
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