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This argument just doesn’t seem quite compelling to me. It also can be placed on pretty much any equipment learning algorithm; I don’t see why This really is specific to neural nets. If this is just intended to clarify why it's okay to overparameterize neural nets, then that makes a lot more feeling to me, although then I’d say anything like “with overparameterized neural nets, many different parameterizations instantiate a similar operate, and Hence the ‘effective parameterization’ is decrease than You could have thoughtâ€, rather than stating just about anything about Kolmogorov complexity.
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We do have a great deal of empirical proof that easy features without a doubt have even bigger volumes in parameter-Place (exponentially even larger volumes, in actual fact). See especially the 2nd and third paper connected in the OP.
As an illustration, if a file could be compressed quite a bit by a ZIP file encoding, then that file has minimal Kolmogorov complexity, although not all reduced Kolmogorov complexity strings could be compressed by ZIP specifically.
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Specifically, If your inductive bias arrived from SGD, we would expect that bias to go away if we replaced SGD with random sampling. In random sampling, we sample an initialization in the neural community, and when it's got zero training error, then we’re completed, in any other case we repeat.
"Uncomplicated" features within the LZ sense are So types that respond to binary vectors in (approximately) a predictable way,. Â What does it suggest to get a functionality to answer binary vectors within a predictable way?
In addition, most features that in shape a presented established of training information won't generalise properly to new knowledge. And still, if we educate a neural community we will usually receive a purpose that offers superior generalisation. What is the mechanism guiding this phenomenon?
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Ok, I do think a confusion right here is that I (as well as OP AFAIK) Will not discuss a similar factors as 파워볼 you do when utilizing the term "purpose". Solomonoff induction is about systems (generally Turing devices) and from your comment it looks as if the sense of capabilities you take. But capabilities as I'm working with below (and I'm very sure This can be the meaning while in the quotation) is just an enter/output relation.
So it would not seem sensible to claim that two features are equivalent (in the way in which your talking about a íŒŒì›Œë³¼ë¶„ì„ minimum of), simply because they always differ on some enter (or they'd be precisely the same operate). Then again, two applications can be equivalent in which they output the exact same issues (they compute related capabilities).
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