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https://nitishpuri.github.io/posts/books/a-visual-proof-that-neural-networks-can-compute-any-function/ https://nitishpuri.github.io/posts/books/a-visual-proof-t

https://nitishpuri.github.io/posts/books/a-visual-proof-that-neural-networks-can-compute-any-function/ https://nitishpuri.github.io/posts/books/a-visual-proof-that... This is a rather intuitive mathematical proof that neural nets can emulate all functions in many dimensions. Knowing integrals (Calc 102) would help. With this information it’s either that self-driving is eventually possible or human brains are not mathematically representable (i.e. something akin to a soul). Meanwhile, the data collection/storage is getting better (all Teslas are continually testing FSD and reporting failure cases, synthetic generation of “good and unique” perfectly labeled data[0] is only a year or two “old”). Sensors/cameras are improving (and have a lot more room to improve). The compute hardware is getting better and cheaper (analog computers[1], TSMC 2nm and beyond, Apple/Google/Teslas neural cores, etc). Additionally, given Waymo is already in production without humans in PHX it’s arguable that we already have “autonomous vehicles”. We now just need them to improve slightly and for Waymo or similar to test in the top 25 cities in the US. Which is mostly a matter of capital and time not technology limits. Maybe weather will be an issue for a few more years/decades - but even if Waymo only operated in Summer, I’d be happy to reduce my Lyft costs - and with enough data and maybe better sensors the neural nets will be able to handle weather too. Especially if the car just goes slow. [0] https://youtu.be/j0z4FweCy4M https://youtu.be/j0z4FweCy4M [1] https://youtu.be/GVsUOuSjvcg https://youtu.be/GVsUOuSjvcg [2] https://www.cnbc.com/2022/01/08/heres-what-it-was-like-to-ride-in-a-waymo-with-no-driver-in-phoenix.html https://www.cnbc.com/2022/01/08/heres-what-it-was-like-to-ri...

simion314 5y ago
>This is a rather intuitive mathematical proof that neural nets can emulate all functions in many dimensions. Yes, but the problem is we don't know what function we want to approximate. So it is like interpolation you give it some points and you get an approximation that is good enough around those points but probably very wrong if you are far away of the points. We don't even know how many layers and neurons are needed so it seems to be a brute force approach, throw more data and more hardware and when stuff goes wrong maybe throw more data. But one day a Tesla might go on a different environment and maybe people have different hats and goes to shit because those hats were not in the training data, we don't have like in other sciences bounded errors.

simion314 5y ago

>This is a rather intuitive mathematical proof that neural nets can emulate all functions in many dimensions. Yes, but the problem is we don't know what function we want to approximate. So it is like interpolation you give it some points and you get an approximation that is good enough around those points but probably very wrong if you are far away of the points. We don't even know how many layers and neurons are needed so it seems to be a brute force approach, throw more data and more hardware and when stuff goes wrong maybe throw more data. But one day a Tesla might go on a different environment and maybe people have different hats and goes to shit because those hats were not in the training data, we don't have like in other sciences bounded errors.