HN user
damn, the rhetoric in this thread put out by (I presume) Americans is like in 2006 when I got my first Neostrada and I first joined Mac vs PC wars
dont mean to offend, just didnt realize things were this rabid over the big pond
Yeah, my writeup is I guess what you get when you first remember it _wrong_ and then need to overcorrect.
ok but she was talking about riemann
know what this will be about without reading
Python 3.12-style type annnotations are a good example imo, no one uses the type statement because dataset inertia
The first and only time I've ever felt like I really know Chinese was when I came across the phrase '洋汽扑鼻' in "Fortress Besieged" by Qian Zhongshu. It literally means 'the breath of the sea assaults the nostrils". It's a joke on how fashionable and in demand everything Western was in China in the 1920s. For me it's just laugh-out-loud-for-10-minutes funny. I've tried to explain it to literal dozens of my friends and now I know not to even try.
I really don't think it's all that different, sorry. The difference is that there is a more direct and established way of talking about these things in China, because it has such a long history of bureaucracy and everyone got used to these dnyamics over thousands of years, but even in places like Sweden you can have guanxi. It boils down to doing something for a member of your ingroup strictly because he's in your ingroup.
I mean even the word 关系 and "network" have the same etymology. 系 = threads of silk arranged in a pattern.
Well that's all fun and games until you start putting off paying Internet bill for two weeks because it turns out that you misconfigured your password app and it actually didn't save your password to the utility service provider and you realize you have no internet one day and you have a school assignment ugh and maybe your credit score gets 0.5% lower and yeah it's all very much your fault. "But you can just be more careful! Handle stuff like this as it arises!" Yeah, sure, just like during Communist times you could easily get more than one pound of coffee per half a year if you're just careful and note when it's available in stores as a drop-in
I believe this whole Apple vs Linux debate is perfectly analogous to the West vs East Germany debate, to the point that almost all intuitions/arguments for the latter are perfectly reusable in the former
I have now read the paper and it alone is enough to make me seriously consider devoting significant amount of my time to the author's project. Here's why:
In my introductory statistics class, I learned that a independent and identically distributed sample is a sequence of random variables X[1], ..., X[n], all of the same signature Omega -> (usually) R. All of them are pairwise independent, and all of them have the same distribution, e.g. the same density function. Elsewhere in probability I have learned that two random variables that have the same density function are, for all intents and purposes, the same.
For all, really? Let's take X[i] and X[j] from some i.i.d. random sample, i != j. They have the same density, which leads us to write X[i] = X[j]. They are also independent, hence
P(X[i] in A, X[j] in A) = P(X[i] in A)*P(X[j] in A),
but X[i] = X[j], so
P(X[i] in A, X[j] in A) = P(X[i] in A, X[i] in A) = P(X[i] in A), so
P(X[i] in A) in {0, 1}.
This was a real problem for me, and I believe I had worse results in that statistics class than I would have if the concept was introduced properly. It took me a while to work out a solution for this. Of course, you can now see that the strict equality X[i] = X[j] is indefensible, in the sense that in general X[i](omega) != X[j](omega) for some atom omega. If you think about what needs to be true about Omega in order for it to have two different variables, X[i] and X[j]:Omega -> R, that are i.i.d, then it will turn out that you need Omega to be a categorical product of two probability spaces:
Omega = Omega[i] x Omega[j]
and X[i] (resp. X[j]) to be the same variable X composed with projection onto first (resp. second) factor. This definition of "sampling with replacement" is able to withstand all scrutiny.
Of course, just like in Buzzard's example of ring localization, it was all caused by someone being careless about using equality.
I really like this. I remember my first serious math book, which was this old-school set theory and topology book, and being all excited about learning set theory up until I encountered iterated Cartesian product, and was forced to accept that ((x, y), z) and (x, (y, z)) are supposed to be indistinguishable to me. An answer on StackExchange said that "you will never, ever, ever need to worry about the details of set theory", but I still did.
I kinda have this idea that while psychedelics like LSD are the easiest to catch a ride with, it is specifically tea that can get you furthest. When I was reading "Dream of the Red Chamber" some of the descriptions of tea drinking were really psychedelic, like being transported into a different realm of heavenly purity that permeates everything with effortless perfection, etc. Certainly I never experienced anything like this with any drug.
Yeah, and we have more than measure zero -- the subsets of the input space on which a fully ReLU MLP is linear are Boolean combinations of hyperspaces. I was coming at it from the heuristic that if you can triangulate a space into a finite number of easily computable convex sets such that the inside of each one has some trait, then it's as good as saying that the space has this trait. But of course this heuristic doesn't always have to be true, or useful.
I just skimmed through it for now, but it has seemed kinda natural to me for a few months now that there would be a deep connection between neural networks and differential or algebraic geometry.
Each ReLU layer is just a (quasi-)linear transformation, and a pass through two layers is basically also a linear transformation. If you say you want some piece of information to stay (numerically) intact as it passes through the network, you say you want that piece of information to be processed in the same way in each layer. The groups of linear transformations that "all process information in the same way, and their compositions do, as well" are basically the Lie groups. Anyone else ever had this thought?
I imagine if nothing catastrophic happens we'll have a really beautiful theory of all this someday, which I won't create, but maybe I'll be able to understand it after a lot of hard work.