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We do have loads of empirical proof that simple functions in fact have bigger volumes in parameter-House (exponentially larger volumes, actually). See In particular the 2nd and 3rd paper linked from the OP.
Especially, I'm cautious of the focus on measuring complexity for features between finite sets, such as binary functions.
(That is an exaggeration but I believe it is actually directionally correct. Surely when I study the title "neural networks are basically Bayesian" I used to be considering anything incredibly distinct.)
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I am not sure how to reconcile that with one other arguments in that article for why it should be unique, even though, such as the experiments that Peter And that i did.
I need to Observe that SGD surely does come up with a contribution towards the inductive bias, but this contribution does seem to be really tiny when compared to the contribution that comes from the implicit prior embedded while in the parameter-perform map. Such as, in case you evaluate Figure 6 during the In the direction of Details Science submit, you are able to see that diverse versions of SGD give a rather unique inductive bias.
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The assertion can be real as long as we keep the which means of "objects" constant as we change the complexity measure.
 But the instance exhibits the claim about complexity actions will only hold if our translation is "ok" in some sense.  If we don't have any strategy what "good enough" means, anything is missing with the Tale.)
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