The h Bar

12:00 AM

Also have you tried training activations to any extent? I'm going through this DL course and it was mentioned that you could use leaky ReLU and optimize the "leakiness"...though I suppose that's technically more model selection than training. Sounded like an interesting concept though

enumaris

12:29 AM

yeah, I've used leaky relu's before, but leaky relu's are not trained. The alpha parameter is a hyperparameter

I think you mean a Parametric Relu?

@danielunderwood also I'm not sure which part you mean "looks bad" lol, what you said seemed fine to me.

welp, my bounty officially expired. On a good note, the question got me 80 rep so I got 80% of my rep back lol.

danielunderwood

Yeah it was more of the hyperparameter even though I called it training...I wonder if there's a way to systematically include it in the loss or something

And saying lol to them saying no...it was meant to be a league joke though

enumaris

Ah

There is a way to systematically include training that leaky parameter

it's called a Parametric Relu unit

all you do is allow $\alpha$ to be trained...you just open up backprop to that variable as well

danielunderwood

hmmm neato!

enumaris

keras.io/layers/advanced-activations

see the PRELU section

see, I know my DL...stupid openai just didn't see it...(I'm bitter lol)

user400188

@Slereah thanks for the answer :)

danielunderwood

12:42 AM

Ahh I think I've actually used that before...I just had no idea what I was doing at the time lol

enumaris

XD

important to know what it is you're doing :D

on my autoencoder, the PRELU worked better than the RELU and SELU and ELU units

user400188

hmm.... how to reference a chat room?

enumaris

but it still wasn't good enough to get me the results I wanted

danielunderwood

Yeah I think I tried all of those without much knowledge about them

Still haven't messed with encoders yet though

enumaris

ah

danielunderwood

12:45 AM

I'm almost done with the first DL course in the sequence, which has gone by fairly quickly. Though this one is pretty much just overexplaining linear algebra

enumaris

I built an autoencoder as a stand in for a RBM...since the dl4j peeps didn't support RBMs anymore on account of "everybody just doing autoencoders now"

the courses are good overall tho :D

kartik c.p

john now is it thaat time .can i meet you in some other room

enumaris

JR probably sleeping

danielunderwood

Yeah I imagine I probably won't be able to breeze through the other courses quite as easily. I do really like the jupyter notebooks instead of matlab in his other course

Do these courses cover autoencoders/BM/GANs?

enumaris

1:42 AM

I don't recall, but I don't think so...

Secret

3:28 AM

Slow science

Slow science is part of the broader slow movement. It is based on the belief that science should be a slow, steady, methodical process, and that scientists should not be expected to provide "quick fixes" to society's problems. Slow science supports curiosity-driven scientific research and opposes performance targets. == See also == "Publish or perish" == References == == Further reading... ==

I cannot see what can go wrong other than research will be so slow to fix urgent world problems

user400188

4:24 AM

Do mathematical physicists conjugate the scalar on their bra's or kets when they take it out of an inner product?

I know pure physicists conjugate the scalar on the bra, and pure mathematicians conjugate the scalar on the ket, but I've no clue what someone from both camps will do.

dm__

6:11 AM

Anyone here?

John Rennie

@dm__ morning :-)

dm__

Morning! I've got an electrodynamics question, care to ponder with me?

Anonymous

6:32 AM

@dm__ Spare us the suspense :P

Anonymous

Just ask

dm__

alright, here's the setup...

say we've got a dielectric in a cylinder of length L, which has uniform polarization P inside. if we straddle the boundary with a square path, the line integral is PL. however, I'm unsure how to extract what the curl would be AT the boundary, which is what I'm trying to extract

the curl is everywhere else zero, inside and out, so I'm pretty sure it must have a delta function dependence

and unnecessary for me to say dielectric in a cylinder. just consider the whole thing a dielectric.

and the path is rectangular X)

John Rennie

9:08 AM

Could someone flag this answer? I'm still barred from flagging.

-1

A: Torque for a door

Torque was one of the Monkee wrenches.

Captain Bohemian

9:21 AM

what does "dimensionless" in "dimensionless gauge coupling" mean? I have seen two places in which this phrase is used.

"... through the dynamical Higgs mechanism the W,Z-bosons acquire a mass via the Higgs condensate and at energies below a couple of 100 GeV they can no longer be excited from the vacuum and consequently the corresponding weak interactions freeze out. We are then left with only the electro-magnetic interactions between the quarks, leptons and the photon described by Quantumelectrodynamics and the strong interactions between the quarks and the gluons described by Quantumchromodynamics (QCD).

The parameters of the latter theory are the masses of the six quark flavours and the dimensionless gauge coupling."

the above is one place where I see "dimensionless gauge coupling".

John Rennie

Presumably it means the coupling constants like the fine structure constant ...

Captain Bohemian

@JohnRennie you mean dimensionless gauge coupling means the coupling is described only by constants (without any variables) so there is no dimension/degree of freedom involved)?

John Rennie

9:37 AM

Well that's how the fine structure constant works ...

Captain Bohemian

9:50 AM

@JohnRennie but in Wikipedia the running coupling seems to be referred to as dimensionless gauge coupling, as in "There are many quantum field theories which, while not being exactly scale invariant, remain approximately scale invariant over a long range of distances.

Such quantum field theories can be obtained by adding to free field theories interaction terms with small dimensionless couplings. For example, in four spacetime dimensions one can add quartic scalar couplings, Yukawa couplings, or gauge couplings. Scaling dimensions of operators in such theories can be expressed schematically as Δ = Δ 0 + γ ( g ) $\displaystyle \Delta =\Delta _{0}+\gamma (g)$...

Generally, due to quantum mechanical effects, the couplings g
do not remain constant, but vary (in the jargon of quantum field theory, run) with the distance scale according to their beta-function."

John Rennie

Well yes, the fine structure constant, and the other coupling constants, aren't actually constant because they change with energy. However they are dimensionless, and I would guess they are what is being referred to in your quote.

Slereah

Also the "bare" fine structure constant is a constant

Captain Bohemian

@JohnRennie so energy is not counted as a dimension/degree of freedom?

like Hubble constant is not really a constant because it depends on time but time is not counted.

John Rennie

@CaptainBohemian dimensionless just means the coupling constant has no units ...

John Rennie

11:05 AM

@DavidZ is this really unclear? It seems to me to be asking a clear and specific question.

David Z

11:26 AM

@JohnRennie Hm, it seemed unclear to me - I mean, I thought there was no indication of why the asker is not able to understand that the expression given in the question represents a Lorentz-invariant quantity. But I suppose that's not such a slam-dunk case that it calls for a mod hammer.

I'll reopen it but in its current form I would very much like to see the community put it on hold.

Also your comment there should have been an answer ;-)

user351417

@DavidZ Nope, that's link-only :P

John Rennie

@DavidZ I guess the OP is a beginner and doesn't understand much about SR. The question seems rather lacking in effort, but it seems reasonable to me. You'll note I've found a similar Q/A though it isn't a duplicate.

David Z

@Chair Ah, so it is. I misread it.

@JohnRennie I agree that the OP seems to be a beginner and not to understand much about SR, but we differ in that I don't think it's a reasonable question (at least not for this site).

John Rennie

I guess it's not immediately obvious to me why the inner product of two four vectors is a Lorentz scalar. Well, it is but only because I already know the answer. I mean for someone who doesn't already know the answer it's not obvious.

David Z

I can get behind that, but I would expect a bare minimum level pf effort to look up the answer. Even just reading a relevant Wikipedia page, or whatever happens to come up in the top few search results, should give some information the asker could have used to define the question better.

Secret

11:46 AM

The Periodic Table Song (2018 UPDATE!)

►

may be a bit too old, but this new version is much better

In other news, I wonder when we will see g block elements soon

(Bonus points for being one of those youtube videos that makes me smile since a very very long time)

Slereah

ww3.haverford.edu/physics-astro/songs/lehrer/elements.htm

It's a 70 years old idea

Slereah

1:16 PM

Welp

Time to send more PhD applications!

John Rennie

2:13 PM

@DavidZ I think it's worked out OK. Emilio has written a very nice answer and the OP commented that he now understand it.

user929304

3:01 PM

@ACuriousMind Hi, let me know when you're around for a tiny QM question. It's about how we compose Hilbert spaces, sometimes we have a macroscopic variable, say A, describing the properties of a subsystem S with Hilbert space H_S. The Hilbert space of the entire system can then be written as tensor product between H_S and H_R where H_R denotes the Hilbert space of the reservoir (i.e. remaining d.o.f's). But I've heard the composition is not always so. For example, (...)

@ACuriousMind (...) in a crystal, the long wavelength phonons can be considered as our subsystem S here, while the short wavelength phonons belong to the reservoir. Apparently, then, the Hilbert spaces are not just factors of the Hilbert space H of the entire space. Which begs to ask, why in this case we no longer have a relation like $H = H_S \otimes H_R$ ?

enumaris

4:38 PM

hmmm

@danielunderwood I got a cool idea for something to do with GANs... could lead to a paper... you interested in working with me on it? You can be first author if we do write a paper and you do more of the work :P

Slereah

Hey @ACuriousMind

enumaris

I'm getting back the urge to work on more ML/DL stuff in my free time...less CSGO...

danielunderwood

@enumaris I don't know much about GANs yet, but I'm interested

"less CSGO" is what I told myself too many times during college lol

enumaris

I can teach u the high level details about them lol

there might be some implementation details that I might leave out cus I forgot or something...

danielunderwood

My knowledge of them so far is pretty much "One NN generates samples and optimizes to create samples the other misclassifies"...or something like that?

I do have Goodfellow's section on generative algos open to read, but haven't read it yet

enumaris

4:46 PM

one neural net creates samples <--- the generator, and a discriminator network tries to identify if the generated samples are genuine or not

One should pre-train the networks though

the discriminator especially can start off as pre-trained

danielunderwood

Is the end goal to generate realistic samples or to improve the discriminator?

enumaris

the end goal is for the generator to win

produce samples so real that it's impossible to distinguish

The issue that I have with a generic GAN though is that the input to the generator is just a noise matrix

you're supposed to generate an image starting with just noise

what I want to do, is to attach a RNN pre-processing pipeline to the input of the GAN so that instead I'm inputting some representation of a caption

and have the GAN reproduce the caption in an image

so basically reverse the image-captioning problem using RNN's attached to a GAN

I think it could be done, and I'm not aware of someone else doing it. Of course, we'd have to do a literature search to see if it's been done before...and if it has, we could improve on their architecture or something.

danielunderwood

hmmm sounds interesting

enumaris

Are you familiar with the image-captioning problem?

basically you put an image and a NN captions that image

like "a group of children playing frisbee in the park"

danielunderwood

Well I'm googling it at the moment lol

enumaris

4:53 PM

XD

I can provide my 1080Ti as processing power to train the network

if the network requires more processing power than that to train then we are in a pickle...lol

You ever watch I-Robot?

danielunderwood

I have a GPU that I could use as well, though it's just a wimpy 980Ti

Uhh the one with Will Smith? I did many years ago

enumaris

there's a scene where the robot draws a "dream" for him

this is gonna be like the NN that accomplishes that :P

not the dreaming part

only the moving a concept into image part

danielunderwood

Is this similar to the way services automatically tag images?

Though that's just a tag and not an entire caption

I suppose that could be done without the whole GAN part

enumaris

Image captioning is similar to like classification

but it generally uses visual attention to focus on parts of the image as it's generating an output

I'm thinking of reversing that process

within the Generator

to use attention to generate parts of images at a time

the architecture should be pretty novel...again, we'd have to do a literature search...

danielunderwood

hmmm I've actually looked at a number of image classification resources in the captioning talk I'm looking through...though I didn't really know what I was doing at the time

enumaris

5:01 PM

we can do some pretty cool stuff man

danielunderwood

This is what I'm looking at at the moment for the captioning problem. Got any literature to give me some background?

enumaris

there's a course on coursera

let me see if I can find it hold on

it's not as good as the Andrew course

danielunderwood

Do people ever do masking for captioning? Like mask then classify that mask instead of just classify the entire image?

enumaris

so I don't recommend paying for it unless you already have a monthly subscription

I think visual attention is like a more sophisticated version of that

danielunderwood

Would COCO be the dataset for such a thing?

enumaris

5:06 PM

I'm not familiar with that dataset

but I think there's gotta be a big data set for the image captioning problem right

we can use the same data set

but just in reverse

danielunderwood

Ahh I've used it before to try masking, but I'm not terribly familiar with it. I figure any paper will mention the dataset used though

enumaris

yeah...I'm not too worried about getting an image captioning data set

there's gotta be a big one out there

one could also generate that data set by using a strong image captioning system

which would give our system a pre-requisite...but...still doable

hmmm...having a hard time finding that course...

oh, here it is: coursera.org/learn/intro-to-deep-learning?specialization=aml

week 4 has GANs in it

but a word of caution, the instructors for that course are not nearly as good as Andrew. They don't explain concepts in as easy to understand way.

danielunderwood

5:21 PM

Yeah I started a GR course from HSE and had trouble. I'll take a look at it

enumaris

maybe just watch the GAN videos lol

danielunderwood

Looks like this may have GANs as well. At least it listed an assignment about them cs231n.github.io

enumaris

I would say, there's no need to use that course as a real course in the sense of starting from week 1 and then going forward and completing

interesting

I'll take a look as well :D

I'm gonna google search to see if there's anybody doing the same thing already

arxiv.org/abs/1605.05396

oh dang -.-

it's been done in 2016 lol

my memory isn't what it used to be...I'm pretty sure I've seen this paper before too LOL

danielunderwood

That's text to image and you're talking about image to text though?

enumaris

no I'm talking about text to image lol

Image to text is image captioning - that's a pretty standard problem

and they use GAN's in text to image too...so...

danielunderwood

5:27 PM

Ahh I see

enumaris

what we could do is improve on the architecture and get better results

e.g. by incorporating attention or reverse-visual-attention

danielunderwood

Indeed!

enumaris

with attention mechanisms we could potentially translate much longer descriptions into images

this paper seems to be limited to ~20 word descriptions

~10-15 actually...

I'd definitely read that paper first before doing anything tho lol

and probably look at papers that cite that paper

danielunderwood

Let's just go for the end game of book -> movie

enumaris

lol

I'd be on board with that if you could convince google to let us use their servers for free

danielunderwood

5:32 PM

"we need all the compute power please"

enumaris

no way in hell my little 1080Ti can handle that

even if I bought 2 2080Ti's...there's no chance

even like those 20k computers with like 8 2080Ti's...probably not

danielunderwood

All the cloud providers have some sort of new account credit (and I think AWS even has some sort of research credit)...though that will handle all of a day of GPU training

enumaris

I'm guessing for a problem like that you'd need thousands

using that much compute power will be uber expensive

danielunderwood

Also one semi-related thing I've been interested in is image enhancement, though that's image -> image generation

ACuriousMind

@Slereah hey

enumaris

5:35 PM

holy jeez that paper has 595 citations to it

@danielunderwood like denoising autoencoders?

openaccess.thecvf.com/content_ICCV_2017/papers/…

here's another paper about text to images

using stacked GANs

a more sophisticated model than the first one

danielunderwood

I'm not sure what a denoising autoencoder is, but it sounds more or less reasonable

ACuriousMind

@user929304 I don't know anything about crystals, but if you e.g. just take the space of all photon states and partition it by wavelength, then the problem is that that space is already the sum of all finite tensor products of the one-photon space with itself

In that case, the total photons space is the sum of all finite tensor products of the "short wavelength one-photon space" with the "large wavelength one-photon space", but the one-photon space is not the tensor product of the two.

danielunderwood

Are birds/plants standard for this type of task or is that just what they've been able to handle?

enumaris

@danielunderwood basically you add noise to input images in an autoencoder and have it generate the normal version

and in the future it can be used to generate denoised images

@danielunderwood not sure there's a "standard" at that task yet lol, there's some papers on it but it's still obviously an area of research

openaccess.thecvf.com/content_cvpr_2018/CameraReady/0842.pdf

dammit, even attentional GAN has been taken -.-

forget it then, I think it'd be too hard to come up with something more novel in that field atm lol

all my ideas are taken already grrr...I also thought up variational autoencoder for collaborative filtering...but lo-and-behold some research group already did it for netflix sonofabitch

danielunderwood

I'll let you know when I come up with a revolutionary new idea :D

enumaris

5:49 PM

sounds good XD

Slereah

@ACuriousMind is your university cool

ACuriousMind

@Slereah sure

enumaris

it is in winter

ACuriousMind

I mean, I loved studying here, and in theoretical physics I think in Germany only Munich is better in some respects.

enumaris

I guess my only consolation prize is that the concepts I think up are actually doable - as evidenced by the people who already did it lol

danielunderwood

5:53 PM

Just think up improvements to your ideas lol

enumaris

I bet sparse attention is also a thing

Emilio Pisanty

so... seriously? this made HNQ?

3

Q: Why is the scalar product of two four-vectors Lorentz-invariant?

Why is the scalar product of two four-vectors Lorentz-invariant? For instance, given two four-vector $A^\mu$ and $B^\mu$, so their scalar product is $A\cdot B=A^\mu B_\mu=A^\mu g_{\mu\nu}B^{\nu}$. Why is $A^\mu g_{\mu\nu}B^{\nu}$ Lorentz-invariant?

enumaris

I better research that

ACuriousMind

@EmilioPisanty The power of many answers :P

The formula should optimize for quality, on many sites it actually optimizes for controversy, and on ours it often optimizes for rather basic questions because many physicists love trying to explain the basic things in their own words...

3

enumaris

The scalar product is Lorentz Invariant because it is a scalar

tautology man strikes again!

Emilio Pisanty

5:57 PM

@ACuriousMind looks like, yes

@ACuriousMind true dat

on a separate track, though

-4

Q: What does conceptual mean?

I've told to come here by another user after my question was put on hold a few days ago for being "off-topic". What does "conceptual" mean? It's a word I see floating around a lot on this site and it's never explained. Ever. I asked the aforementioned user what it meant and they directed me here...

discussion scope questions homework-and-exercises

I really disagree with the duplicate closure

I'm a bit reluctant to reopen-hammer it

ACuriousMind

Yeah, it's not really a duplicate, I would agree. But I'd also be reluctant to unilaterally reopen.

Emilio Pisanty

eh, I'm just going to go for it and apologize

With due apologies for the unilateral action - I really don't think that this is a duplicate. There's a lot to criticize here in AustereTiger's complete disregard to reading the site policies before going on to rudely dismiss and criticize things s/he hadn't even attempted to understand, despite explicit pointers to go and read $-$ but the way to deal with those flaws is to downvote. Or can the close-voters explain why they think that this is an exact duplicate? — Emilio Pisanty 8 secs ago

enumaris

@danielunderwood maybe we should be more ambitious and work on "sparse attention"...unfortunately it's a super vague concept and I don't see a clear path forward unlike the GAN concept lol.

the upshot is, because it's so vague, there's no chance someone already "did it"...since we can always just work on the part that's "not done"

I was gonna devote research to this area at openai, but since they rejected my application I guess that's not gonna happen

danielunderwood

Is there much of anything towards selectively using attention currently?

enumaris

I haven't seen much on it

google scholar doesn't show too many relevant searches on the first page

I think sparse signals in general is a real huge area that needs to be explored

sparse reward signals in reinforcement learning

sparse attention

sparse training sets

one-shot learning

Slereah

6:13 PM

@ACuriousMind would you recommend doing a theiss there

danielunderwood

I've never even heard of most of those things. I know of sparse in the case of matrices and such. Would sparse in these cases include noise as well?

enumaris

I'm using sparse in a very vague sense

sparse reward signals is the problem in Reinforcement learning where your rewards are few and far between

it's hard for an agent to learn to do well in those cases because there's just too much randomness in its initial choices

a RL agent, if it's learning from scratch, would basically try out a bunch of random actions until it "stumbles" upon actions that gives it rewards

in the case of sparse rewards, the agent has a hard time learning.

ACuriousMind

@Slereah I...think so? Feels a bit weird if I recommend doing a thesis shortly after not doing one myself :P

enumaris

This is evidenced by games like montezuma's revenge where you have to take a lot of steps, get keys, find items, etc., before getting to your goal.

I think the current method to work around that problem is by "reward shaping" in the sense of putting intermediate rewards for intermediate actions that lead to the goal action.

but that process is pretty much a manual process

danielunderwood

Is there a standard RL resource?

And I suppose the MNIST for RL is asteroids or something?

Well not so much general resource as a standard starting place

Semiclassical

6:24 PM

@EmilioPisanty "The poster being a jerk may be grounds to close a question, but you still need to close it for the right reasons."

something like that?

enumaris

@danielunderwood I read the book, I'll find it, hold on

drive.google.com/file/d/1opPSz5AZ_kVa1uWOdOiveNiBFiEOHjkG/view

I read an earlier draft

but it's a good book

I'll probably buy it on amazon to support the authors since I read the entire thing as a draft lol

Sha Vuklia

guys, temperature is defined with the volume of the system held fixed. i'm confused then why the thermometer's operational definition works, since the liquid is expanding?

is it just that it's approximately the same?

enumaris

dang, it's textbook priced -.-

meh, still worth it

danielunderwood

Awesome I'll take a look

enumaris

but yeah you can prolly read the google drive ebook for a while (?) before they take it down...I dunno if they are gonna take it down at some point

ACuriousMind

6:30 PM

@ShaVuklia "temperature is defined with the volume of the system held fixed" - what definition of temperature do you mean?

Semiclassical

@ShaVuklia Presumably you have in mind the following: $T=(\partial U/\partial S)_{V}$

enumaris

it's uploaded by the authors though so there's no piracy concerns

Sha Vuklia

@Semiclassical yes, this definition indeed

danielunderwood

Wooo DL course is done!

Semiclassical

but if you do a legendre transform to get to the enthalpy, you also have $T=(\partial H/\partial S)_{p}$

enumaris

6:31 PM

@danielunderwood all 5 of them? that was fast lol

Semiclassical

and since $H=U+pV$, one has $T=(\partial U/\partial S)_p+p (\partial V/\partial S)_p$

enumaris

whoop that book will come by tomorrow :D

danielunderwood

oh no just the first

enumaris

ah

danielunderwood

though I think it took 4 days since I took a couple off, which isn't too bad

Semiclassical

6:32 PM

I feel like there's a name for that $(\partial V/\partial S)_p$ term, hmm

hmm. something about what I wrote doesn't make sense

$(\partial(pV)/\partial S)_p$

i guess that should still just be $p(\partial V/\partial S)_p$

Sha Vuklia

yea I think so too

user929304

@ACuriousMind Hi, you've perfectly captured what I m trying to understand, and your photon example stands as equivalent to mine (for the purposes of these discussions). I'm still struggling to understand the part where we say "...is already the sum of all finite tensor products of the one-photon with itself." Could you please explain this part at a much more basic level? What is different about partitioning a space according to wavelength here, as opposed (...)

(...) to partitioning according position and spin where then we can take a tensor product of the two (assuming here there are position and spin operators, even though they can be tricky matters for photons).

Sha Vuklia

alright thanks, I hadn't heard of legendre transforms, but they seem useful. for now I'll just take your word for it @Semi

Semiclassical

you haven't seen internal energy vs. enthalpy vs. free energ(ies) yet?

Sha Vuklia

uhm, I know the definition of enthalpy, and.. all I know is that when we consider internal energy in our thermal physics course, we usually think of thermal energies, because we want to work with the equipartition thm

but I think free energies will be treated soon, I think I saw it somewhere

ACuriousMind

6:36 PM

@user929304 Alright, I'll try: 1. There is a one-photon space of states $H_1$, with a momentum (=frequency=wavelength, for photons) basis $\lvert p\rangle$.

Semiclassical

oh, right, one of the maxwell relations is $(\partial V/\partial S)_p = (\partial T/\partial p)_S$

dont' think that's very helpful here though

Sha Vuklia

hm no, we definitely haven't had that

ACuriousMind

2. The space of "all photons states" is $H_\text{tot} = \sum_{i = 1}^\infty \left( H_1^{\otimes i} \right)$, which is the space of states with arbitrarily (but finitely) many photons.

Sha Vuklia

I'm reading from Schroeder's introduction to thermal physics

Semiclassical

you'll get to those eventually, then

enumaris

6:38 PM

@danielunderwood some of the future courses are quite good in the sense that there's no other courses like them

Sha Vuklia

don't know if you're familiar with it, but we basically treat the first 5 chapters

enumaris

like the structuring ML projects course

Semiclassical

I think he may talk about enthalpy in the first chapter?

Sha Vuklia

and I saw that the later chapters get a bit more formal

enumaris

it's pretty unique

Semiclassical

6:38 PM

not sure tho

Sha Vuklia

@Semiclassical that is correct

just to talk about heat capacity with pressure held fixed

Semiclassical

right

Sha Vuklia

and to give an intuitive idea what it means

danielunderwood

@enumaris awesome! Looks like this next one is hyperparameter tuning, so I imagine it will go pretty quickly too

Semiclassical

one thing to note: $\Delta H=\Delta U+\Delta (pV)$

Sha Vuklia

6:39 PM

yep

ACuriousMind

3. We may partition the one-photons space at some arbitrary momentum $p = p_0$ into two summands $H_1 = H_{1+} \oplus H_{1-}$, where $H_{1+}$ has as its basis all states $\lvert p\rangle$ with $p>p_0$ and $H_{1-}$ all states with $p<p_0$ (I don't care what you do with $p=p_0$, put it whereever ;) ).

enumaris

yeah, of the 5 courses, pretty much 3 are "meaty" model-learning courses

Semiclassical

so if there's not much change in $pV$, then the change in H and U are basically the same

enumaris

one for dense NN's, one for ConvNN's and one for RNNs

Sha Vuklia

but in the case of the thermometer, there's a significant change in V right?

enumaris

6:40 PM

then hypermarameter tuning is good for learning how to generally go about training the models, and there's a course on structuring ML projects to learn how to do that

Semiclassical

seems like it would be, yeah

Sha Vuklia

but it's good that you pointed out the fixed-pressure thing

I should keep in mind that relations for fixed pressure exist, because they are useful

Semiclassical

of course, we're also acting like it's obvious to compute $T=(\partial U/\partial S)_p$ experimentally

which seems sorta dubious

ACuriousMind

4. Note that it is not the case that $H_1 = H_{1+}\otimes H_{1-}$. This is because $H_{1+},H_{1-}$ are not subsystems of the one-photon system - if you measure a single photon's momentum, it's always either in $H_{1+}$ or in $H_{1-}$. For true subsystems, you should be able to measure a state of both subsystems for every measurement.

Sha Vuklia

so we just change volume (possibly) and energy

why is it dubious? you mean it's difficult, or ambiguous?

Semiclassical

6:42 PM

well, how well can you measure changes in entropy?

Sha Vuklia

oh lol yea you're right

I forgot you wrote "experimentally"

Semiclassical

Probably the better point to start with is $C_p=(\partial H/\partial T)_p = (\partial U/\partial T)_p +p(\partial V/\partial T)_p$

user929304

@ACuriousMind Very interesting! thanks a lot, you are giving very valuable explanations, I just need time to process it still :/

Sha Vuklia

well, I haven't seen how to compute the temperature of a liquid anyways. we've only treated (einstein) solids, low-density (monatomic) gases, and paramagnetic materials, because we can find explicit expressions for $S$

@Semiclassical yea, I'm getting this idea that heat capacity is partly defined just because it's so useful in experiments

as opposed to some of the more theoretical definitions

Semiclassical

yeah, it's not fun to define these things

typically you more define them based on useful experimental properties

Sha Vuklia

6:46 PM

yea that makes sense

Semiclassical

fun fact, though: there are such things as constant-volume thermometers

ACuriousMind

5. However, the tensor product is distributive: $H_\text{tot} = \bigoplus_{i = 1}^\infty \left( H_1^{\otimes i} \right) = \bigoplus_{i = 1}^\infty \left( (H_{1+} \oplus H_{1-})^{\otimes i} \right) = \bigoplus_{i = 1}^\infty$ Now $\left( H_{1+} \oplus H_{1-}\right)^{\otimes i} $ expands to a sum of $i$-fold tensor products where $H_{1+}$ and $H_{1-}$ occur in all possible orders. The sum over those then is the "sum of all possible tensor products of the short and long wavelength space".

Sha Vuklia

oh lol:d

Semiclassical

c.f. en.wikipedia.org/wiki/…

Sha Vuklia

a paramagnet?:p

oh

Semiclassical

6:47 PM

that's under the assumption of the ideal gas law tho

Sha Vuklia

that's not a problem right, as long as you keep the density low

Semiclassical

so i don't know how well that works as a model of a mercury thermometer

Sha Vuklia

ah

danielunderwood

@enumaris yeah I'm really interested in the structuring one. Like I'm comfortable with structuring normal software, but ML stuff always seems to not really fit into the same type of structure

Sha Vuklia

my guess is that the expansion in volume can be neglected, so that it's at least correct to first-order approximation

Semiclassical

6:48 PM

maybe

Sha Vuklia

but that's just a guess to make my life easier for now

enumaris

tbf, ML projects is a relatively new area so Andrew is giving you his experience in doing it

Semiclassical

what one seems to have access to experimentally is the volume as a function of temperature at fixed pressure

so $V(T,p)$

enumaris

It's not nearly as structured as software dev though...like agile or sprint or w/e other models you're gonna try to use. I suppose you could implement those models to ML, but that's not really what is gone over in that course.

Sha Vuklia

for a liquid?

Semiclassical

6:50 PM

for a mercury thermometer

Sha Vuklia

ah

Semiclassical

in which case you seemingly should be looking at the Gibbs free energy $G=U-TS+pV = G(T,p)$

you won't see that for a while though

Sha Vuklia

i think it will be mentioned in the next chapter or so, but maybe just shortly

because I tought I saw it somewhere

user929304

@ACuriousMind point 5. will take me a while to digest, but if I may already go back to what was said upto point 4.: what is the meaning of \oplus? I only knew about \otimes (tensor prod) for composing Hilbert spaces, (e.g. Hilbert space of 3d position of a particle being written $H= H_x \otimes H_y \otimes H_z$ where $H_i$ is the space of the ith position component. I understand now what was meant by "that kind of partition not being really a partition into true subsystems".

Semiclassical

yeah

Sha Vuklia

6:51 PM

hm alright, well thanks for the input in any case

Semiclassical

np

Sha Vuklia

I feel a bit more at ease, haha:)

danielunderwood

@enumaris well I was more of separating things off into modules/functions/classes reasonably so you don't have a huge chunk of messy stuff

ACuriousMind

@user929304 It's the direct sum. It's the more straightforward way to combine vector spaces - the direct sum of an n-dimensional and an m-dimensional vector space is just an $(m+n)$-dimensional vector space.

enumaris

@danielunderwood that is not what is meant by "structuring ML projects" in that context then...

danielunderwood

6:54 PM

ahh I suppose I'll actually figure out what it means when I get to it

enumaris

Andrew goes over like the stages of a ML project - inception, getting a data set to work with, building a simple model, refining, diagnosing the model...stuff like that

how to actually structure the code is not gone over

danielunderwood

Oh then that's helpful too

enumaris

From a data science perspective, how the code is actually structured is not the main focus

getting the results you want is the main focus

Semiclassical

@ACuriousMind simple example: If you think of your first vector space as "degree n-1 polynomials in x" (an n-dim vector space) and your second as "degree m-1 polynomials in y" (an m-dim vector space)

user929304

@ACuriousMind ah I see! I still don't get (from a very naive pov) why $H_1 = H_{1+}\oplus H_{1-}$ and not $H_1 = H_{1+}\otimes H_{1-}$ ... :( in other words, what kinds of partitionings of a space lead to an $\oplus$ composition as opposed to $\otimes?$ (in the context of QM and Hilbert spaces)

enumaris

6:55 PM

but well structured code definitely does help with getting the results you want

Semiclassical

then the direct sum of those is just the vector space of polynomials in x,y where the degree in x is at most n-1 and the degree in y is at most m-1

then the basis vectors are all $x^j y^k$ with $j=0,1,\ldots n-1$ and $k=0,1,\ldots,m-1$

enumaris

My code is structured into the level of classes...but I haven't actually had to deal with class inheritance much for example. Since I haven't had to write a whole framework like Keras. I expect that as I write more of my RL library, I will have to get into that game more.

danielunderwood

Yeah I think well-structured code is important to being able to iterate quickly and distribute the knowledge once you're done

Semiclassical

wait. crap

this is the tensor product

faaaail

enumaris

@danielunderwood for sure

danielunderwood

6:57 PM

Hey let me know if you want help with a RL lib too

enumaris

oh yeah, we could also work on that XD

are you familiar with pytorch?

cus that's the backend I'm using for it

Emilio Pisanty

@Semiclassical kind of, I guess. OP may be a jerk but that's not a closure reason at all.

Semiclassical

ugh ignore me, i'm being foolish

@EmilioPisanty well, it could be a closure reason. for instance, if they're proceeding in an abusive way

ACuriousMind

@user929304 Maybe it helps to think in terms of bases: If you take a space $H$ and a basis $v_i$, then you can split the basis into two sets (e.g. by taking one set to be the $v_i$ up to $i < i_0$ for some $i_0$, and the other the $v_i$ starting from $i \geq i_0$.). The two sets span two subspaces and the total space is their direct sum. Take for instance $\mathrm{R}^3$ - it is the direct sum of the 2d space spanned by the $x$ and $y$ basis vectors and the 1d space spanned by the $z$ basis vector.

Semiclassical

but that's a different matter than it being closed as a duplicate

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