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The paper talks a bunch about things such as SGD remaining (Virtually) Bayesian as well as the neural network prior obtaining reduced Kolmogorov complexity; I discovered these being interruptions from the key level.
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I think The best theoretical result could well be to point out that SGD on neural nets is definitely an approximation of Solomonoff Induction (or something like SI), and also the approximation receives improved since the NNs get bigger and deeper. But I have however to find out any idea that connects neural nets/ SGD to anything like small programs.
We do have empirical data which displays the neural network "prior" is biased towards minimal-complexity functions, and some arguments for why it would seem sensible to be expecting this to be the case -- see this new blog put up, and my comment listed here.
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Checking out figure 5d, we do in fact see generalization error to the buy of five% from SGD samples (the y-axis is just not pertinent for the estimate listed here).
Typically, we care about NN generalization on problems exactly where the input Area is continual, generally R^n. Â The authors argue that the finite-set results are relevant to these problems, simply because one can always discretize R^n to acquire a finite established. Â I don't Assume this captures the forms of purpose complexity we treatment about for NNs.
I'd be interested to hear your take on this remark higher than, and that is speaking about compressibility, which to me appears like kolmogorov complexity.
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I concur with the summary. I'm primarily just clarifying 파워볼 what my check out is of the strength and General part in the Algorithmic Data Principle arguments, since you explained you located them unconvincing.Â
" Â In the event you treatment about getting somewhere around proper according to some metric, this sales opportunities you to level-distortion concept.