Neural networks are very non-linear. The blessing and curse of non-linearity is its usefulness while escaping what mathematical logic inherently is able to model. So yes, I strongly assume there will never be a mathematically sound theory that predicts deep learning in any meaningful way. Same problem with everything non-linear. From two-body to chaotic systems, biological interactions to the stock market. All just wishful thinking until Mathematicians give up and instead continue to play around in their well-defined esoteric spaces.
I think you conflate several ideas of understanding here. We don't have good ways of predicting chaotic systems, but we often know a lot about them. Just knowing they're highly sensitive would be hard to confirm without math.
you don't seem to have a background in mathematics. A huge(and growing) body of work exists for every example you gave. Obviously mathematicians are interested in nonlinear systems
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Neural networks are very non-linear. The blessing and curse of non-linearity is its usefulness while escaping what mathematical logic inherently is able to model. So yes, I strongly assume there will never be a mathematically sound theory that predicts deep learning in any meaningful way. Same problem with everything non-linear. From two-body to chaotic systems, biological interactions to the stock market. All just wishful thinking until Mathematicians give up and instead continue to play around in their well-defined esoteric spaces.
I think you conflate several ideas of understanding here. We don't have good ways of predicting chaotic systems, but we often know a lot about them. Just knowing they're highly sensitive would be hard to confirm without math.
you don't seem to have a background in mathematics. A huge(and growing) body of work exists for every example you gave. Obviously mathematicians are interested in nonlinear systems
So you're saying Hari Seldon's psychohistory is BS?