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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Replying to @Plinz
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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Replying to @mattgiammarino
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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Replying to @Plinz
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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Replying to @mattgiammarino
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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Replying to @Plinz
Ok yes makes sense! Each model is enmeshed in others and they’re sorta mutually contingent. And I suppose each model is also a composition of other models (or automonia?).
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Yes. Most models work by reducing the data to a few free parameters, by identifying trends. Where the trends change, they find meta-trends describing where the local trends apply, which leads to nested models.
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