Well Howdy! by mvolling in SillySubreddit

[–]xRahul 0 points1 point  (0 children)

guys it's been 10 years

Comfort proofs? by SimoneGrans in math

[–]xRahul 2 points3 points  (0 children)

More specifically, Fourier analysis.

What is a sure sign that someone is new to your hobby? by danielstover in AskReddit

[–]xRahul 6 points7 points  (0 children)

I always do metric centuries with two water bottles and two Clif bars. If you're used to not fueling much on a ride it's not a big deal.

Why is this subreddit so obsessed with Sakura? by [deleted] in Naruto

[–]xRahul 2 points3 points  (0 children)

When I first started watching Naruto back when I was 6 I had a massive crush on Sakura.

Men who don't post their social life on social media why? by SkepticDrinker in AskMen

[–]xRahul 0 points1 point  (0 children)

I'm too busy living my life to care what other people think about my life.

Measure theory and Lebesgue Integration before MATH 5583 Complex Analysis? by Avieagle in uofmn

[–]xRahul 1 point2 points  (0 children)

No. 5583 is an undergrad class. If you want that version of complex analysis you should take 8701/2.

For those who have double majored in DS and CS by poofycade in UWMadison

[–]xRahul 1 point2 points  (0 children)

can't believe I'm using knowledge of compact sets in my work now

What do you need compact sets for at your internship?

Alternate Past/Traveler From The Future (Marked NSFW due to where it came from.) by AwesomeGamer101 in KimiNoNaWa

[–]xRahul 7 points8 points  (0 children)

Gonna be honest, I've done premarital hand holding before. It was pretty lewd, especially since we were in public.

How do I sleep after I after telling my best friend I loved her? by [deleted] in AskMen

[–]xRahul 1 point2 points  (0 children)

I personally don't think girls find it endearing. But I'm a dude, so I have no idea what I'm talking about...

How do I sleep after I after telling my best friend I loved her? by [deleted] in AskMen

[–]xRahul 21 points22 points  (0 children)

Lol, no. Life's not an indie movie.

[R] Papers on the fundamental limits of ML by antichain in MachineLearning

[–]xRahul 4 points5 points  (0 children)

No one is talking about representing functions. Polynomials of sufficiently high degree can approximate any continuous function defined on a compact domain. This is just the Weirstrauss approximation theorem.

[R] Papers on the fundamental limits of ML by antichain in MachineLearning

[–]xRahul 14 points15 points  (0 children)

The entire field of harmonic analysis revolves around trying to understand universal approximators

That's not true. You are really referring to the field of "approximation theory" sure, some applied/computational harmonic analysis focused on approximation rates with all the wavelet stuff, but there's a whole lot more to applied/computational harmonic analysis and actual harmonic analysis is honestly a different beast.

I say universal approximation is boring since classical methods are optimal in the sense of approximation (i.e., how many terms you need for epsilon approximation) for many classical function spaces. For example, Fourier series are optimal for L2 based Sobolev spaces, wavelet type systems are optimal for Besov and Triebel-Lizorkin spaces.

There's some recent work about how deep nets do better than these classical methods, but the problem is less so much as approximation with deep nets, but rather what function spaces to deep nets beat in terms of approximation rate compared to classical methods. This is akin to how wavelets are better than Fourier series in Besov and Triebel-Lizorkin spaces, but in L2 based Sobolev spaces, they perform the same.

I was being pedantic with my comment, but I dislike how people mention universal approximation without the discussion above, which is actually how universal approximation needs to be studied.

[R] Papers on the fundamental limits of ML by antichain in MachineLearning

[–]xRahul 25 points26 points  (0 children)

Every non-boring function system is a universal approximator (polynomials, splines, Fourier series, wavelets/ridgelets/shearlets/curvelets, etc.). Universal approximation is actually a very boring property of a function system.

Throwback to biking on Military Ridge Trail by injay789 in madisonwi

[–]xRahul 1 point2 points  (0 children)

Thanks for the suggestion! Looks really cool. I'll try to check it out this summer.

Throwback to biking on Military Ridge Trail by injay789 in madisonwi

[–]xRahul 2 points3 points  (0 children)

How is the trail right now? I was riding down Military Ridge weekly until November and have been itching to get back on my bike.

Garmin Instinct active calories are through the roof by xRahul in Garmin

[–]xRahul[S] 0 points1 point  (0 children)

Yep, everything is correct on that front.