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New sphere-packing record stems from an unexpected source

quantamagazine.org

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Re: New sphere-packing record stems from an unexpected source

#161

Post by aleph_minus_one »

doubledamio wrote: post #153
thorum wrote: post #26

Earlier quoted context omitted.

Some ideas are too complex to explain accurately in simple terms. You can give someone a simple explanation of quantum chromodynamics and have them walk away feeling like they learned something, but only by glossing over or misrepresenting critical details. You’d basically just be lying to them.

To me, every profession—from software engineering to farming—has its complexities, yet most professionals can explain what they do in clear terms. When academics say they can’t offer a basic explanation, it often feels like an attempt to protect their status or avoid the effort—if not a kind of intellectual arrogance. Yes, the topics are challenging—you don’t need to throw in quantum buzzwords to convince me—but simp…

If you have such an opinion, explain some advanced papers of Peter Scholze to me.

Re: New sphere-packing record stems from an unexpected source

#162

Post by aleph_minus_one »

zmgsabst wrote: post #123
Dylan16807 wrote: post #117

Earlier quoted context omitted.

If you have a very small neural network, you can fully understand and explain how it works. As you increase the detail of a description, it reaches a point where nothing is missing.

As I pointed out, eg, the high number of correction terms when trying to tune the model to actual particle accelerator data is evidence that our model is missing something. (And some things are plain missing: neutrino behavior, dark matter, dark energy, etc.) In the same way that a high number of epicycles was evidence our theory of geocentrism was wrong — even though adding epicycles did compute increasingly accurat…

> As I pointed out, eg, the high number of correction terms when trying to tune the model to actual particle accelerator data is evidence that our model is missing something. (And some things are plain missing: neutrino behavior, dark matter, dark energy, etc.)

This is rather a problem of the standard model. Physicists will immediately admit that something is missing there, and they are incredibly eager to find a better model. But basically every good attempt that they could come up with (e.g. supersymmetric extensions of the standard model; but I'm not a physicist) has by now (at least modtly) been falsified by accelerator experiments.

Re: New sphere-packing record stems from an unexpected source

#163

Post by aleph_minus_one »

m4tthumphrey wrote: post #146
clickety_clack wrote: post #7

I have trouble explaining to my parents how my job is a real thing. I can only imagine trying to explain ‘I study shapes, but only ones that don’t jut inwards’.

I just say “I work with computers”. I get the nod of “oh right nice” and that’s it. Done.

> I just say “I work with computers”.

This is a suitable description of possibly 70 % of all jobs.

Re: New sphere-packing record stems from an unexpected source

#164

Post by aleph_minus_one »

fcanesin wrote: post #99

I feel like mathematicians should be able to do a second doctorate level degree a few years after their first PhD, that must be in a adjacent field of their own, but not the same.

Beside the habilitation example of rando234789 (https://news.ycombinator.com/item?id=44498702), in Russia (and Ukraine) there indeed exist two "doctorate levels": кандидат наук [Candidate of Sciences] and доктор наук [Doctor of Science].

Re: New sphere-packing record stems from an unexpected source

#165

Post by shakna »

tharkun__ wrote: post #158
shakna wrote: post #149

Earlier quoted context omitted.

I think the negotiation signal being sent by "all jargon" is "fuck off". It's not an attempt to gauge what level the other person is using. It's a blank wall, being thrust towards them.

It seems like dumbing it down or immediate heavy jargon with people you don't know are just both equally bad options. What's wrong with asking their level of experience with the topic? Sure, with parents you know the level. I'm talking "other strangers" you meet outside of a context where some familiarity would be expected (like at a conference one might assume at least some form of knowledge and ability to just have…

> What's wrong with asking their level of experience with the topic?

Nothing. That's precisely the point. Giving a wall of jargon, isn't asking if someone is familiar.

Re: New sphere-packing record stems from an unexpected source

#167

Post by teiferer »

zmgsabst wrote: post #103
tbrownaw wrote: post #77

Earlier quoted context omitted.

Take for example entanglement. The math that describes it is known precisely. Specific implications of this are known. There's no information transfer, there's no time delay, etc. And yet lay people keep incorrectly thinking it can be used for communication. Because lay-audience descriptions by experts keep using words that imply causality and information transfer. This is not a failure of the experts to understand w…

> This is not a failure of the experts to understand what's going on. > We don't have a model of why it works / if there's a more comprehensible layer of reality below it. Counterpoint: You’ve just admitted they don’t understand what’s going on — they merely have descriptive statistics. No different than a DNN that spits out incomprehensible but accurate answers. So this is an example affirming that QM isn’t understo…

QM isn't less well understood though than Newton's mechanics. Neither cover the "why". But both provide a model of the world, the model (!) is very precisely understood and it matches observations in certain parts of reality. Like all reasonable scientific theories do. They have limits, and beyond those limits they don't apply, but that doesnt mean they are not understood. It's reality that is not sufficiently well understood and by coming up with more and more refined models/theories, we keep approximating it, likely without ever having a "fully correct" theory encompassing everything without limits. (But that's ok.)

Re: New sphere-packing record stems from an unexpected source

#169

Post by asboans »

Someone wrote: post #159

FTA: “in 100-dimensional space, his method packs roughly 100 times as many spheres; in a million-dimensional space, it packs roughly 1 million times as many“ Nice example of how weird large-dimensional space is. Apparently, when smart minds were asked to put as many 100-dimensional oranges in a 100-dimensional crate as they could, so far, the best they managed to do was fill less than 1% of its space with oranges, an…

“Fill less than 1% of its space” becomes a very counter intuitive statement in any case when discussing high dimensions. If you consider a unit n-sphere bounded by a unit cube, the fraction occupied by the sphere vanishes for high n. (Aside: Strangely, the relationship is non monotonic and is actually maximal for n=6). For n=100 the volume of the unit 100-sphere is around 10^-40 (and you certainly cannot fit a second sphere in this cube…) so its not surprising that the gains to be made in improving packing can be so large.

Re: New sphere-packing record stems from an unexpected source

#170

Post by Scene_Cast2 »

dotancohen wrote: post #100
Scene_Cast2 wrote: post #33

Earlier quoted context omitted.

They weren't sparse, they were dense but the "density" was quite non-uniform (think typical learned ML vectors). Not too far from an N-dimensional gaussian (I ended up reading research on quantizing Gaussian distributions, but that didn't help either as we didn't have a perfectly gaussian thing).

I see, thank you. Another thing that I'm sure you explored, and I'd love to hear how it went, would be to rearrange the elements in the vectors such that perhaps the denser parts could be more contiguous, and the sparser parts could be more contiguous, on average. That sounds like something that would be easier to compress. Were the distributions such that a rearrangement like this might have been possible? Or were t…

What ended up launching is a fancy product quantization based on k-means. Some of the tricks were storing magnitude separately (i.e. removing the mean) and rearranging dimensions based on variance (and/or rotation based on PCA) for PQ to work better.

I also remember trying to fit a distribution so that I can generate synthetic data (not for a lack of data, but more for understanding the problem space better). The synthetic data quantized pretty differently - my guess is that it's because of random areas of density and sparsity.

I'm not quite following your exact rearranging idea though. Not sure if the above answers the question.

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