hodgehog11

16 ms·

271.
by hodgehog11 1y ago
Interesting, this was the big 'a-ha' moment in the grad course I took on the subject. Surgery was clearly important too, but this seemed to be more apparent from Hamilton's work. The W functional was what provided the control
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by hodgehog11 1y ago
This is one of those things that seems easy in retrospect, but wasn't particularly obvious at the time. 1. Proving existence to a differential equation using a numerical approximation is quite a bit more difficult than it seems at firs
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by hodgehog11 1y ago
For sure, I've never used a language of this paradigm. I'm also bothered by the fact that I don't have a single good reason why I should, and would love to know if somebody has one. The currently given reason is curiosity. I
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by hodgehog11 1y ago
For those like me who are wondering "why?", the tutorial answers this up front: "I don't know why anyone would choose to learn this unless they're a very specific kind of masochist" Well, there are all types in
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by hodgehog11 1y ago
I feel like a great deal more credit should be given to Cauchy and his school, but I understand the tale is long enough. The Peano axioms are pretty nifty though. To get a better appreciation of the difficulty of formally constructing the i
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by hodgehog11 1y ago
To add to this, I think it is important to recognise that this is not fundamentally a Deepmind project; engineers from Deepmind came to help with the computational aspects to bring the error down after the lead and last authors brilliantly
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by hodgehog11 1y ago
They find a very good approximate blowup solution (non-smooth) using a NN. When the solution is good enough, you just need careful fixed point theory to infer an actual solution.
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by hodgehog11 1y ago
It will take another few months at least, and the rest of the argument will comprise a fair few pages. But the hardest part is over. When working toward a problem of this magnitude, it is natural to release papers stepwise to report progres
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by hodgehog11 1y ago
So for reference, I am a mathematician, I work in probability theory. I don't work in optimisation theory, but saw a talk a few days ago by a prominent member in that field ranting about the obsession with pointless bounds when industr
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by hodgehog11 1y ago
It's based on knowledge of the related estimates, applying similar techniques to geometric problems, knowledge of all the prior works that lead to the current work, and speaking with members of the team themselves. They are much furthe
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by hodgehog11 1y ago
Um, okay? Isn't that how most optimisation involving AI is supposed to go? Perhaps some much needed context. Mathematicians are not stupid; we are very much aware of all the existing forms of genetic optimisation algorithms, cross entr
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by hodgehog11 1y ago
This is absolutely true, but it still makes use of the advantages and biases of neural networks in a clever way. It has to, because computationally-assisted proofs for PDEs with singularities is incredibly difficult. To me, this is not too
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by hodgehog11 1y ago
Unfortunately, this doesn't fully transfer over for math. The Fields Medal has an age limit on it for example, based on an ancient premise that old mathematicians can't make new incredible discoveries. It's ridiculous though,
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by hodgehog11 1y ago
Something else to add is mathematical discovery. There is a team that is very close to solving the Navier-Stokes Millenium Prize problem: https://deepmind.google/discover/blog/discovering-new-soluti... The cynists
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by hodgehog11 1y ago
> We need more of these. > Available data is 0 for most things. I would argue that we need an effective alternative to benchmarks entirely given how hard they are to obtain in scientific disciplines. Classical statistics has gone very
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by hodgehog11 1y ago
I agree that there is power in numbers for science, but not all science is lab work. Sometimes the bottleneck is purely computational.
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by hodgehog11 1y ago
As someone who works in the field, it really doesn't feel like more money (proportionally speaking) is going to this. A little bit is done here and there for PR. The number that are working on net positive applications for AI is still
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by hodgehog11 1y ago
Here is some evidence for you then: https://arxiv.org/abs/2411.00566 Not published just yet are experiments for finding solutions to mathematical problems traditionally found with SAT solvers, at much larger scale than
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by hodgehog11 1y ago
Exact same story; Fedora has been so much more wonderful than I expected. Made me realise just how far the Linux desktop has really come these past years while Pop OS languished. I've tried the alpha, and while bugs were few, Cosmic do
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by hodgehog11 1y ago
As an Australian, I can say that Kmart here is an absolute powerhouse. They sell highly curated goods made in China for very cheap, it's a dream for young people on a budget. Poor delivery services here pushes people toward brick and m
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by hodgehog11 1y ago
Four months? Six months? Is that supposed to be a long time? I know people that have been in this situation for nearly two years now. Forget hopeless, it's a bottomless pit of despair. I don't know how to help them, and neither do
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by hodgehog11 1y ago
That was a lot of fun, and far too addictive to play on a weekday! I feel like you are forced to get the power upgrades at first to get past the larger roadblocks before the fire wall hits you, but maybe this is avoidable if you're fas
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by hodgehog11 1y ago
No, it isn't a solution, but at least young people would be ingesting literature, which I would argue is a far cry better than the brainrot YouTube videos targeting kids. That's an assessment of the status quo though, we should ab
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by hodgehog11 1y ago
Does this consider audiobooks? Personally, I have been reading fewer physical books and have preferred to listen to them instead. This comes as my eyesight deteriorates, but I can imagine that for others, listening to books over audio can b
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by hodgehog11 1y ago
This makes sense on its face, but the flaw in the logic here is the implicit assumption that current procedures extract all information available in the datasets. We know this is not even remotely close to being true. Many decades ago, stat
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by hodgehog11 1y ago
Okay, I am happy to hear that is not what you were implying; a bit extreme, but that's how I read your comments in light of the reality, taking the skepticism to its apparent conclusion. I genuinely did not intend to provide a straw ma
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by hodgehog11 1y ago
Do you really think that Friendly Jordies, Jeff Geerling, Second Wind, Red Letter Media, Brodie Robertson, Game Grumps, Vinesauce, Dead Meat, Dark Viper, and Linus Tech Tips, for example, are in the same Discord channel (Friendly Jordies is
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by hodgehog11 1y ago
Uh, there have been dozens of videos of senior YouTube creators who have independently voiced alarm about this within the past few days. It's now been long enough since the algorithm change that statistical time series analyses can det
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by hodgehog11 1y ago
Hmm, I don't see where they have suggested this, could you point to where this is? If they do argue for this, then I would also disagree with them. Modelling those things is a separate problem to emitting plausible text and pursuing on
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by hodgehog11 1y ago
I mean no disrespect, as I'm no more fond of OpenAI than anyone else (they are still the villains in this space), but I strongly disagree. > It's useful as a term of understanding. No it isn't. I dare you to try publishing

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