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That is a bit of a tangent, though the Levin sure is in fact about Kolmogorov complexity. It can be a reasonably uncomplicated theorem; the evidence is constructive, and generally demonstrates that a presented functionality file which corresponds to quite a few parameters in the parameter-House cannot be as well intricate, by setting up a straightforward software which computes file. Pretty approximately, If your parameter-space is finite and discrete, then we could assemble a Huffman code for that purpose space (where the distribution above the operate-space is the distribution that corresponds into the uniform distribution about the parameter-Room).
I concur that this arguably could be mildly deceptive. One example is, the correspondence between SGD and Bayesian sampling only definitely retains for many initialisation distributions. In case you deterministically initialise your neural network for the origin (i.
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The comparison with Solomonoff induction strikes me as Completely wrong, because Solomonoff induction adapts to new data, While "most features that in shape a presented set of coaching details will likely not generalise perfectly to new info." generally signifies that the function is learned and therefore set when offered new facts.
This makes it really probably that DNNs are "only executing interpolation", in certain sense, rather than extrapolation. (This previously appeared rather probable dependant on scaling curves, and the gaussian approach design offers us a 2nd line of evidence.)
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Largely, we care about NN generalization on issues where by the input space is continuous, frequently R^n. Â The authors argue the finite-set results are relevant to those challenges, mainly because you can always discretize R^n to secure a finite set. Â I don't Assume this captures the forms of perform complexity we care about for NNs.
The main place, as I see it, is basically that functions with fantastic generalisation correspond to huge volumes in parameter-House, Which SGD finds functions with a probability about proportional to their quantity.
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