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Of these ten^10k features, the wide vast majority could have really bad accuracy about the test set. Hence, if we attempted to do inference by choosing a random operate that matches the instruction knowledge, we'd Virtually certainly get pretty bad generalisation (in fact, we might expect to obtain the identical precision just like random guessing).

The rest of the comment is about stuff that I didn't have a powerful feeling on, so I'll go away it for Zach to answer if he wishes.

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We can sometimes be certain that a Finding out algorithm will generalise very well if it can only Convey a restricted list of capabilities (see VC dimensionality). Nevertheless, a neural community is simply too expressive for this rationalization to work (as they can Convey all Those people 10^10k features).

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Such as, in the event you have a look at Determine six during the publish I link, you can see that different versions of SGD do give a slightly distinctive inductive bias. Having said that, this impact seems to be quite tiny relative to what is furnished by the "prior".

Chris (creator from the connected publish) messaged me about these, And that i also checked out the full paper and thought about it some a lot more.

In what sense is definitely the parameter Room of a neural community not finite and discrete? It is often valuable to know floating-place values as continuous, but the truth is They're discrete these kinds of that it looks as if a theorem which assumes discreteness would even now utilize.

I usually do not wish to say that all capabilities with reduced Kolmogorov complexity have significant volumes inside the parameter-Place of a adequately substantial neural network. In fact, I'm able to stage to quite a few concrete counterexamples to this declare. To give just one instance, the id operate certainly provides a very low Kolmogorov complexity, nevertheless it's quite challenging for the (fully linked feed-forward) neural community to learn this purpose (When the input and output is represented in binary sort by a bit string). If you are attempting to know this function by education on only odd numbers then the community won't robustly generalise to even numbers (or vice versa).

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