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It is a little bit of a tangent, nevertheless the Levin bound is really about Kolmogorov complexity. It can be a reasonably easy theorem; the proof is constructive, and in essence reveals that a specified operate file which corresponds to many parameters in the parameter-Area can't be too sophisticated, by constructing an easy system which computes file. Extremely about, When the parameter-House is finite and discrete, then we could assemble a Huffman code for the perform House (exactly where the distribution above the purpose-House will be the distribution that corresponds for the uniform distribution in excess of the parameter-space).
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I don’t think this is in conflict With all the declare in the paper, that is that _most_ of your inductive bias emanates from the architecture and initialization.
But, I do concur which the Levin sure argument doesn’t really capture the “mechanism†of what’s taking place listed here. I can of course only communicate for myself (and never the Others involved with this work), but I visualize the Levin certain argument as basically a more official solution to point out this instinct. I.e., It's really a free argument for why we needn't be surprised that simple functions have larger sized measures in parameter-space, whether or not the argument doesn’t recognize all of the exact facts of how this will work in any individual scenario.
Also, most capabilities that healthy a provided set of coaching details will likely not generalise nicely to new details. And nevertheless, if we coach a neural community we will usually obtain a function that offers excellent generalisation. What is the system powering this phenomenon?
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The common standard, however , you chop it right into a trillion parts over the x axis, and translate the parts to arbitrary destinations in R
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