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This is the little bit of a tangent, although the Levin certain is really about Kolmogorov complexity. It's a reasonably straightforward theorem; the evidence is constructive, and basically demonstrates that a specified function file which corresponds to a lot of parameters within the parameter-Area can not be too complicated, by developing an easy program which computes f. Quite roughly, If your parameter-House is finite and discrete, then we could assemble a Huffman code for your functionality space (the place the distribution more than the purpose-space could be the distribution that corresponds for the uniform distribution around the parameter-House).
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I don’t Believe That is in conflict While using the assert of the paper, which happens to be that _most_ in the inductive bias comes from the architecture and initialization.
There remain some stray items, but I'm now commonly convinced the headline claim is appropriate: the vast majority of inductive bias emanates from the implicit prior to the network's parameter Place.
I am not sure the best way to reconcile that with another arguments in that article for why it ought to be distinctive, while, such as the experiments that Peter And that i did.
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As it is achievable to compress significant-probability occasions utilizing an optimal code for the chance distribution, you may perhaps hope that capabilities with substantial likelihood inside the neural network prior can be compressed much more than capabilities with lower chance.