Generally, we treatment about NN generalization on troubles in which the enter Area is constant, usually R^n. The authors argue which the finite-established results are related to those troubles, since one can always discretize R^n to acquire a finite set. I don't Assume this captures the sorts of perform complexity we care about for NNs.
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We do have loads of empirical evidence that easy capabilities in truth have even larger volumes in parameter-space (exponentially more substantial volumes, in actual fact). See Primarily the 2nd and 3rd paper connected from the OP.
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I am not sure I concur with this particular -- I think Kolmogorov complexity is usually a appropriate notion of complexity With this context.
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You'll find a variety of priors about features for which we could estimate the exact posterior. (E.g., Gaussian procedures.) However, performing Bayesian inference on these priors doesn't execute in addition to neural networks on most datasets. So understanding SGD is Bayesian is just interesting if we also understand that the prior is exciting.
But when you encode the inputs as vectors of duration n and feed them into a design, the layers with the model have weights that happen to be also n-vectors.
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So, I concur that there are certain features with low Kolmogorov complexity that a neural community Usually can't "see" thoroughly. I also Consider one could body a lot of the exploration on creating new neural community architectures as becoming about building neural networks in a position to "see" additional styles of features.
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