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I concur that this arguably may be mildly deceptive. One example is, the correspondence among SGD and Bayesian sampling only seriously retains for some initialisation distributions. When you deterministically initialise your neural community to your origin (i.
We do have loads of empirical proof that simple features indeed have even bigger volumes in parameter-House (exponentially greater volumes, in truth). See especially the 2nd and 3rd paper linked from the OP.
That is just suitable. That actual case in point would be a case of higher circuit size but reduced Kolmogorov complexity.
I agree it is not vacuous. It feels like you're primarily stating exactly the same argument I gave but in various terms. Can you convey to me what is Improper or missing from my summary in the argument?
I feel Chris has now updated the In direction of Data Science weblog submit being much more crystal clear, based on the discussion you experienced, but I'll make some clarifications here too, for the advantage of Many others:
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But any time you encode the inputs as vectors of size n and feed them into a product, the layers of the product have weights which might be also n-vectors.
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this hypothesis, or give a theoretical argument for it of the sort "Right here's why, presented what we learn about math and about complexity principle, basic features need to delight in even bigger quantity in parameter-Room.
S) follows with the figures, at the least not to more than enough of the extent for being "strong proof" in opposition to the assert that SGD is the principle source of induction bias.
Do you do have a very good reference to the Levin certain? My attempts at finding a relevant paper all unsuccessful.
Numerous of these figures clearly show awfully substantial divergence from equality, and i am not viewing any statistical evaluate of healthy. Eyeballing them, It truly is obvious that there's a strong plenty of relation to rule in inductive bias while in the community architecture, but that doesn't rule out inductive bias in SGD also.