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+--- Thread: Artificial Neural Networks vs. Kneser (/showthread.php?tid=1709)
Artificial Neural Networks vs. Kneser - Ember Edison - 02/19/2023
I don't think I need to repeat again the various difficulties we encountered with the Kneser method of getting very close to base 1 and Shell-Thron-region.
Quote:If you need to, click on
https://math.eretrandre.org/tetrationforum/showthread.php?tid=1232 -> to Shell-Thron-region and irrational rotation
https://math.eretrandre.org/tetrationforum/showthread.php?tid=728&pid=7465#pid7465 -> to 1
Welcome more additions!
While I was running Stable-diffusion on my GPU to produce pornographic images, something occurred to me:
Why don't we use Neural Networks to facilitate the numerical computation of the Kneser method?
After all, there is already the precedent of AlphaTensor.
I think we have at least two ways to utilize Neural Networks:
1. Putting hope in the Universal approximation theorem, neural networks are simply used as a kind of super Newton method.
2. Is there some parameter of Kneser's method that can speed up the solution/increase the accuracy by guessing an approximation? If so, use a neural network to train out these parameters.
If the topic of neural networks has been discussed on the forum before, please let me know.
RE: Artificial Neural Networks vs. Kneser - Gottfried - 02/19/2023
(02/19/2023, 04:16 PM)Ember Edison Wrote: Why don't we use Neural Networks to facilitate the numerical computation of the Kneser method?
After all, there is already the precedent of AlphaTensor.
I think we have at least two ways to utilize Neural Networks:
1. Putting hope in the Universal approximation theorem, neural networks are simply used as a kind of super Newton method.
2. Is there some parameter of Kneser's method that can speed up the solution/increase the accuracy by guessing an approximation? If so, use a neural network to train out these parameters.
If the topic of neural networks has been discussed on the forum before, please let me know.
Hello Ember, don't know whether this matters your intention: one of my first readings on tetration 2007 has been Lars Kindermann's doctoral thesis on Neural Network method to tetration. Maybe you know this or maybe that doesn't matter for your intention.... Anyway, the paper is online in case you're interested: I've been a complete greenhorn in tetration and understood nearly nothing that years ago, and so I cannot say, whether there was some relation to Kneser's method considered at all.
RE: Artificial Neural Networks vs. Kneser - Ember Edison - 02/19/2023
(02/19/2023, 04:52 PM)Gottfried Wrote: Hello Ember, don't know whether this matters your intention: one of my first readings on tetration 2007 has been Lars Kindermann's doctoral thesis on Neural Network method to tetration. Maybe you know this or maybe that doesn't matter for your intention.... Anyway, the paper is online in case you're interested: I've been a complete greenhorn in tetration and understood nearly nothing that years ago, and so I cannot say, whether there was some relation to Kneser's method considered at all.
Wow. That's a bit of a long history, lol. After all, there are new results on the Universal approximation theorem that have only been obtained in the last few years, like https://arxiv.org/abs/2006.00625.
I would like to continue to illustrate the relationship between neural networks and Kneser.
The Universal approximation theorem claims that we can approximate any continuous function with a neural network, and the only complex tetration we need is smooth. The next thing to do is just to hammer the nail with the newest hammer.
As for the second route, I have already made it clear.
If there are intermediate variables that can be decomposed in the Kneser's method: getting estimates of these variables will speed up the iteration speed/valuation accuracy of the Kneser's method itself, then one can try to compute these intermediate variables using a neural network.
This gives us a chance to replicate the success of AlphaTensor. We need to have a deeper understanding of the Kneser's method.
Both routes necessarily cost a lot of CPU time, some GPU time and storage space, consume a lot of power and generate carbon emissions. And most valuable of all, human energy.
RE: Artificial Neural Networks vs. Kneser - JmsNxn - 02/21/2023
(02/19/2023, 04:16 PM)Ember Edison Wrote: ....
While I was running Stable-diffusion on my GPU to produce pornographic images, something occurred to me:
...
Lmfao! Ember!
I actually used to mod video games in highschool, and the biggest mod I ever did got bought out by Microsoft; because I sped up their decryption protocol. And the mod was just to make the video game characters naked! Lmao! Not supposed to talk about it though, because I signed an NDA
It's true when they say the heart of technological development is in Porn.
RE: Artificial Neural Networks vs. Kneser - Ember Edison - 02/22/2023
(02/21/2023, 05:58 AM)JmsNxn Wrote: Lmfao! Ember!
I actually used to mod video games in highschool, and the biggest mod I ever did got bought out by Microsoft; because I sped up their decryption protocol. And the mod was just to make the video game characters naked! Lmao! Not supposed to talk about it though, because I signed an NDA
It's true when they say the heart of technological development is in Porn.
I think it's better to say that porn is insurance for advanced display technology: so that the technology can survive the bottleneck phase without being killed by the fucking stock market. (I'm watching you, VR
)
RE: Artificial Neural Networks vs. Kneser - tommy1729 - 02/22/2023
ok this seems to be the REAL reason some people want subsections ...