Re:Differential Equations with Transformers: Deep Learning f...
by whatshisface on Wednesday March 11, 2020 @10:59AM
(#22546359)
For at least a hundred years (as long as symbolic logic has existed, however long that really is) it has been widely known that you can iterate through every single theorem without any special creativity or thinking. The problem with that strategy is that you will spend most of your time on theorems like (not not X => X), (not not not not X => X), (not not not not not not X => X) and so on. What mathematicians actually do is use their human intuition and aesthetic sense to pilot the mechanical formalism towards goals that are worth achieving.
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Re:Differential Equations with Transformers: Deep Learning f...
by vladf on Wednesday March 11, 2020 @01:10PM
(#22547565)
That’s not a really fair way of putting it. Unless you’re suggesting that there’s something deeply magical about our human “aesthetic” intuition why can’t that itself be coded into a set of syntactic indicators (e.g., favor short equations, don’t repeat yourself, connecting theorems otherwise far from each other in some distance metric is valuable) to be used as a search heuristic?
Re:Differential Equations with Transformers: Deep Learning f...
by whatshisface on Wednesday March 11, 2020 @01:13PM
(#22547597)
The human aesthetic can't practically be programmed as a classical algorithm. The human ability to identify cats can't even be programmed as a classical algorithm, that's why neural networks were invented. Maybe a neural network could predict how interesting mathematicians would find a theorem but by that point there's no point for anybody to do anything, even artists.