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I have not seen the paper you link, so I can not comment on it exclusively, but I would like to note the assert "SGD is roughly Bayesian" will not indicate "Bayesian inference would give greater generalisation than SGD". It may possibly at the same time be the situation the neural community "prior" is biased in the direction of low-complexity functions, that SGD around follows the "prior", Which SGD provides some further bias toward low-complexity functions (above and earlier mentioned what's provided by the "prior").
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It truly is legitimate that we don't have a rigorous mathematical evidence for "why" straightforward capabilities must have bigger volumes in parameter-Room, but I can give an intuitive argument for why I feel it would sound right to be expecting this to become the situation.
If SGD is run with early halting, as explained over, then my argument is this is roughly akin to random sampling through an attract concentration of measure in significant-dimensions.
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In what sense is definitely the parameter Room of a neural community not finite and discrete? It is usually helpful to be familiar with floating-position values as steady, but in fact These are discrete this sort of that it looks as if a theorem which assumes discreteness would nonetheless utilize.
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