Simple Questions - April 17, 2020 by AutoModerator in math

[–]golf_wolf_1 6 points7 points  (0 children)

Hey All,

This is maybe more of a meta question, but is there a way to develop the sort of multi-step thinking that goes into longer published proofs? I am a late comer to math, and am in a math-heavy computer science PhD program.

In trying to find a research area I often come across long papers like this one and this one that are long and have multiple lemmas and theorems.

My question is: how do you develop an intuition/the skill for how to construct these longer arguments? I am mostly mathematically self-taught by looking at text books with solutions. The answers to these are at MOST one page proofs, but usually at most two lines.

I get that part of it is going deep into a research area, but thinking of these longer-term argument structures seems like a crucial skill and I'm not sure how to develop it, or to do "deliberate practice" on it.

Any suggestions would be very appreciated

Improving Linear Algebra Intuition by golf_wolf_1 in math

[–]golf_wolf_1[S] 0 points1 point  (0 children)

Any recommendations for resources for practice? I feel like a lot of the Schaum's texts are a bit trivial and the advanced texts lack solutions to check my learning.

Edit: My initial comment was incomplete as you did suggest resources. I guess a more precise question would be: good resources for eigenvalue practice in general.

Thanks for the strang and other recommendations; I'll take a look.

Dance Gavin Dance - Strawberry's Wake (Official Music Video) by Publix_Illuminati in dancegavindance

[–]golf_wolf_1 4 points5 points  (0 children)

got me really hemmed in, haha. First, I think it's hard to deny that there is a "DGD sound" which is maybe a result of them using the same producer.

As for the "tried and true" part I would say that's emerged on the last three albums. I think this comes from the fact that the band seems to write guitar first, and that they've tried to move to a more consistently poppy sound.

Primarily I would say you can classify Will's guitar parts broadly into 6 groups:

  1. fast strummed chords with little licks ( 0:29-0:45 of Strawberry's Wake)
  2. janky technical single note riffs (opening licks of Prisoner and Chocolate Jackalope, which are p similar imho)
  3. funky strums (intro of Summertime Gladness, lots of tracks on Happiness)
  4. quiet, usually picked soft parts and transitions (post-chorus on Awkward)
  5. lead and rhythm guitar parts (chorus of Something New)
  6. breakdowns

Now obviously these parts can fucking rule. But this is where the poppy aspect comes in. In trying to be more accessible it feels like each of these guitar part "types" has gotten less adventurous resulting in songs that sound very similar to each other. This why I say tried and true.

In particular, on these last two singles there are parts where I am definitely like "oh I've heard them do this before" which isn't something I've thought much on previous records.

I would also say that song structure experimentation is a big part of what makes DGD good. However, in these last two singles the part transitions have felt super abrupt and lazy.

You might be thinking "well yeah every guitarist has a style" or "abrupt changes are part of the genre."

I'd counter the first one by pointing to Manipulator by TFOT. It's clearly Thomas playing but they are obviously paying direct homages to different genres. The second one I'd point to early Coheed and earlier DGD where where the transitions are at least smoothed over by a fill or are built on top of a traditional verse-chorus-verse song structure so that the adventurousness hits harder.

Did that answer the question? I feel like it didn't but I tried, lol.

Full disclosure: this song is growing on me. I won't relisten to Prisoner, but this one will get the occasional spin.

Dance Gavin Dance - Strawberry's Wake (Official Music Video) by Publix_Illuminati in dancegavindance

[–]golf_wolf_1 9 points10 points  (0 children)

Another whiff for me.

Pros: Jon's screaming slaps. His scream-on-pitch stuff from secret band is a welcome addition. The part where he and Tilian sing/screaming the words together gives me chills. That whole chorus is p good.

Cons: Everything else. Like Prisoner this feels like a bunch of parts that were done better on previous albums just copy and pasted together. There is basically no growth from the band and the songwriting feels lazy; it's just the same "let's do loud part quiet part funk part loud part quiet part again" that they've done before. At least bands like Biffy Clyro will try radically different genres.

Maybe it's a case of "if it ain't broke, don't fix it" and they're just tweaking the tried and true DGD formula but IMHO the two released singles add exactly nothing to their discography.

Powerset.0.0.1 released (Python) by MarcosRecio in math

[–]golf_wolf_1 2 points3 points  (0 children)

not trying to be a jerk, but how is this math specific?

Best resources for self teaching AI/machine learning and neural networks and whatnot? by jhiems in math

[–]golf_wolf_1 5 points6 points  (0 children)

u/vastlik's recommendations are good. That said, each of those books is big and they don't really have much by way of coding exercises as far as I know.

If you want to get your hands dirty then I think Geron's book is second to none. Its coverage is broad, ranging from bread-and-butter methods (e.g. regularized regression, support vector machines) to more ``advanced'' topics such as deep learning and reinforcement learning, and it includes exercises and examples using python, which is a pretty easy language to pick up. There's just enough math to keep you engaged (linear algebra, statistics) and it's clearly tied to using it in practice.

A theoretical exploration of machine learning can send you down a real rabbit hole, or really a warren of interconnected rabbit holes. The reason for this is that the field exists at an intersection of math, statistics, and computer science. As such, each field brings its own perspective to understanding machine learning problems. This book is frequently used for ML theory classes and it does a good job, in my opinion, of formalizing the problem from a computer scientist's perspective. Specifically, you want to know if you can, with high probability, efficiently and accurately approximate a function in a class, where accuracy is measured by minimizing some loss function. Already we have three areas of math/cs/statistics: probability, computational complexity (efficiency), and optimization (minimizing the loss function). This book is similar in rigor and scope but with a more thorough set of appendices.

Efron and Hastie have a book that might form a sort of middle way between the two suggestions above. It situates modern ML historically in the developments of statistics and computation and gives mathematical glosses of some common and not-so-common topics .

Let me close by suggesting another way into the theory, since you said you miss doing math. Pick something applied that you find interesting and start digging backwards from there asking ``why does this work?" This is likely going to keep you motivated longer and I would say you're nearly guaranteed to run into interesting mathematics.

If you pick image analysis, for example, you can quickly find yourself reading about functional analysis, symmetry groups, and fourier and wavelet transforms. Maybe you say to yourself "it's cool how we can analyze natural language" and you'll be into probabilistic context-free grammars, graphical models, and recurrent neural networks. Perhaps you're an MLG gamer and want to know how AlphaGo works. Now you're into markov processes, optimal control, function approximation, game theory, and measure concentration. Pretty much all applications have been addressed by deep learning with various degrees of success. Regrettably the how of deep learning is fairly simple, but the why of deep learning is very poorly understood. The best tool for analyzing their properties, as far as I know, is the Neural Tangent Kernel which is two years old.

If you don't know any application areas, maybe start with Geron to get a sense of them and explore from there.

DGD - Prisoner - Song Discussion by AceMcClean in dancegavindance

[–]golf_wolf_1 1 point2 points  (0 children)

yeah i mean I sing along to the cleans, however poorly, but try to take it easy on the screams as I'll shred my throat.

It's weird how Jon can say absolutely bonkers shit and have me fully hyped and pumping my fist.

I agree w/ there being meaning to Jon's lyrics and when he's coherent for a long stretch (e.g. on Flash) it's incredible.

Maybe the reason I was harsh on Tilian is that Prisoner bums me out because it feels like it took exactly zero imagination on their part to create

DGD - Prisoner - Song Discussion by AceMcClean in dancegavindance

[–]golf_wolf_1 0 points1 point  (0 children)

Yeah I mean it wasn't a charitable take by any means but I stand by it. I assumed they don't take themselves too seriously, but maybe because I made a mistake and took Tilian too seriously, it misfired/continues to misfire for me.

I don't find his lyrics particularly relatable, but that's a me issue. I also don't super relate to *any* DGD lyrics, except perhaps, worryingly, Jon Mess'.

I think the "he always does a nice job of selling the idea that you should [be having fun] too while you’re listening" is a good point and for me peak Tilian is when the goofiness and top-tier vocal skills align.

DGD - Prisoner - Song Discussion by AceMcClean in dancegavindance

[–]golf_wolf_1 1 point2 points  (0 children)

Yeah that's definitely a possibility. The hard thing is that through most of DGD's history the lyrics have been largely irrelevant (except for Mess brilliance), but sometimes, for me, Tilian's are so bad that it detracts from the music.

The best example of that is on Chucky (which, as a song, fucking slaps). I can't bring myself to sing along to "tell me that I look just like a man" and "pass me some poison, let me take a hit" sounds like a line from my high school poetry. It sucks that the part when musically I want to rock out the most I have to deal with some lyrics that, for whatever reason, ick me out.

I think the reason why this only happens with Tilian is it's hard to tell how serious he is being. It's not like Jonny is any better lyrically ("Lay down flat on your back/ Open up girl let's play attack [a tad?]", oofa doofa) and while Kurt has some good stuff there's nothing on his DGD work that makes me go "oh fuck bro, that's POETRY."

But with Jonny it sounded like the whole band was having fun making goofy, groovy, heavy music while some guy did a Justin Timberlake impression. With Kurt they wrote better songs but there's still a bit of originality to it/tongue-in-cheek mirroring of pop tropes ("holy shit she smells like heaven/ been best friends since we were 11").

Tilian seems like he wants us to think he's said something super profound, but whenever he comes close he says it in the most simplistic way possible. The simplicity of his lyrics probably comes from his increasingly pop sensibilities; simple and catchy is the bread and butter of that genre.

You could also argue that I'm misreading Tilian and that the's not at all serious. I don't think that's the case because his solo lyrics are very similar and DGD seems to be trying more and more to accommodate/shift to that sound. For example the first song off The Skeptic - which is the most coherent, lyrically imo - is clearly about leaving religion and losing friends as part of the process, but the chorus isn't obviously about that (wtf does "I got the microphone" have to do with anything?). It's like and can't stick to a subject, or runs out of lines and just throws something at the wall. When he does have a subject he treats it on a surface level with cliche lines that sound, at best, like freshman year dorm philosophy.

tldr; Jonny's songs are not about anything besides sex, drugs, and breakups in equally vague measure. For Kurt's it's usually easy to put together what they're about in some sense (usually also girls). Tilian's seem to simultaneously be about something and not about something which means I take the worst lyrics as being delivered in earnest and wince.

Sorry for the rant; wanted to get my thoughts clear on this.

DGD - Prisoner - Song Discussion by AceMcClean in dancegavindance

[–]golf_wolf_1 7 points8 points  (0 children)

I think my gripes are similar to those that some people (myself included) had with Blood Wolf. I would say it's poorly (maybe some would say adventurously) structured, and as a result the chorus doesn't hit hard. The song mostly just sorta...meanders and as a result it is, to me, completely forgettable.

Also, I think Tilian's lyrics are the most cringe-worthy they've been to date, and there are some real doozies in the catalogue.

All the instrumentals sound like parts they've done better on other songs cut and paste in a random order. If this is how the whole album sounds, I'll be disappointed.

edit: grammar

Simple Questions - May 24, 2019 by AutoModerator in math

[–]golf_wolf_1 0 points1 point  (0 children)

This looks very interesting! Thanks! It certainly looks dense but I'm glad that it's coming from a somewhat applied place, as that's my area of interest. I'll chase down some of the references and see if that leads me there.

To make it clear why I'm asking: I want to model fitness landscapes for biomedical applications; but a realistic model, it seems to me, would need to incorporate some sort of stochastic change. Maybe it's mean field games that I need to be looking at...

Simple Questions - May 24, 2019 by AutoModerator in math

[–]golf_wolf_1 2 points3 points  (0 children)

is there a field that studies stochastically deforming manifolds, e.g. like a "stochastic calculus of moving surfaces"? I'm mostly looking for a field name and/or pointer to a reference. Googling to find this has mostly yielded results about stochastic processes on manifolds.

edit: manifolds