mjayasur

38:22

pogchamp

gghosal

43:02

In this case are the x values in the D matrix also from the y measurements?

mjayasur

43:41

Is this only for discrete systems?

gghosal

45:54

Ok thank you for the clarification

mjayasur

46:07

Thanks!

Balaji

49:21

How come e isn't anywhere in the expression for p-hat?

mjayasur

49:31

since we are adding in the error vector for a given timestep, shouldn’t we be using x hat instead of plain x vector? I’m sort of confused how the e error vector is coming into play.

Subham Dikhit

50:06

Kind of to add on, then which form for the error is right: the change he just made, or the original form?

Seth SANDERS

51:16

Questions in a moment

mjayasur

51:28

Thanks!

Vainavi Viswanath

51:55

I’m not sure about this but I thought B has dimensions nxm so wouldn’t the transpose have mxn dimensions?

Alberto Checcone

52:18

it does

James Shi

52:46

I think the error is something we’re trying to minimize like with least squares

Balaji

53:04

So the error is y-hat - y?

Calvin Yan

53:30

Should be

Ashwin Rammohan

55:09

why does I go from 1 to R

Ashwin Rammohan

55:21

aren't there n columns?

Aidan Higginbotham

55:32

@Ashwin i think that's a n

Calvin Yan

56:01

No, the number of states n and the number of samples R don’t have to be the same

Aidan Higginbotham

56:24

Oh ignore me then lol

dylanbrater

56:59

If both u and x are n long, then that multiplication doesn’t make sense, bc the two matrices have a n+m height whereas x + u is n+n height

Ashwin Rammohan

57:05

@calvin if he's saying n separate equations, shouldn't i go from 1 to n?

Ashwin Rammohan

57:13

what is R, the number of samples?

Vanshaj Singhania

57:14

wait im pretty sure that's an n @Ashwin @Calvin

Ashwin Rammohan

57:26

@vanshaj ok yeah makes sense

Ranelle

57:30

Doesn’t e increase as we approach the projection of y?

Balaji

57:34

YEah, thanks

Calvin Yan

58:49

Oh I see that now

AJ

01:00:33

So this is finding the best estimate of A and B?

Francisco Galvan

01:00:54

oh, thanks! i actually that was the Reals, good to go

Ayush Sharma

01:01:00

@AJ, yup, I believe that's correct.

AJ

01:01:23

But don’t we get it in some weird transpose form? How do we get A and B back?

Francisco Galvan

01:02:01

i typoed, my mistake, i understand its "n"

Vanshaj Singhania

01:02:12

I think you can reconstruct the matrix with AT and BT

Vanshaj Singhania

01:02:36

and then you know the dimensions n and m so you can visually separate AT from BT and transpose them back @AI

Stephen

01:02:41

so dimension of y is n x L and dimension of D is (n+m )x L?

Stephen

01:02:56

dimension of p is n x (n + m)?

dylanbrater

01:03:42

1

mjayasur

01:03:43

1

Balaji

01:03:43

1?

Vanshaj Singhania

01:03:44

1

Francisco Galvan

01:03:44

1?

Ashwin Rammohan

01:03:45

1

Ranelle

01:03:45

1!

Jake Whinnery

01:04:00

Dimension of the column space

Yimo Xu

01:04:01

The dimension of column space

Balaji

01:04:06

dim range (A)

Jake Whinnery

01:04:08

1

Hamza Kamran Khawaja

01:04:13

3

Ranelle

01:04:28

4! Jk lol

Van Chung

01:05:37

I just want to make sure that Rank is the number of independent column or independent row?

Ranelle

01:05:42

Both.

Kunaal

01:05:47

row rank = column rank

Alberto Checcone

01:05:52

yes. it's the dimension space of all possible outputs

James Shi

01:06:17

[1 2 3] [1 1 1 1 1]

Ranelle

01:06:18

P x Q such that it’s equal to A?

Lily Yang

01:06:21

p [1 2 3]; qt = [1 1 1 1 1]

ayang

01:06:22

[1;2;3] [1,1,1,1,1]

Terrance Li

01:06:22

p = <1,2,3> q = <1,1,1,1,1>

Ranelle

01:06:25

Q^T*

mjayasur

01:06:30

P = [1, 2, 3] qT = [1, 1, 1, 1, 1]

James Shi

01:06:37

no

ayang

01:06:43

l,mao

felixyu

01:06:46

xD

Lucas Huang

01:06:54

the disrespect

Stephen

01:07:04

yes

Lily Yang

01:07:04

any multiples

James Shi

01:07:10

scale p by 2, q by 1/2

Stephen

01:07:13

any scaled version should be fine, right?

ayang

01:07:15

many answers

Vanshaj Singhania

01:07:16

[2 4 6] [.5 .5 .5 .5 .5]

Jake Whinnery

01:07:17

246 and .5.5.5.5.5

mjayasur

01:07:19

yeahz

Ranelle

01:07:23

Any real scalar multiple of Q^T

Calvin Yan

01:10:39

Wouldn’t q^t have to be normalized relative to the first value of the first row?

Vanshaj Singhania

01:11:07

yeah

Yimo Xu

01:13:55

Germany

mjayasur

01:13:56

yeah

Aidan Higginbotham

01:13:59

yes

Ranelle

01:13:59

Deutshland

Lily Yang

01:14:00

yE

Mohsin

01:14:01

yup

Aidan Higginbotham

01:14:02

Germany

Calvin Yan

01:14:02

lmao

toanphan

01:14:02

lol

Lily Yang

01:14:03

germanyy

Lily Yang

01:14:04

wooahh

Bryan Ngo

01:14:08

deutschland

felixyu

01:14:10

Wrong answers only xD

Ranelle

01:14:10

Deu

Kaan Ulupinar

01:14:10

austria

Lily Yang

01:14:11

LOLOL

Vanshaj Singhania

01:14:31

whoaa machine learning on flags??

Ranelle

01:14:40

Deutschhhhland

toanphan

01:14:41

Yep

Jake Whinnery

01:14:46

All I see is not America

Vanshaj Singhania

01:15:01

not America reax only

Ashwin Rammohan

01:15:08

1

Lily Yang

01:15:09

1

Kevin Mo

01:15:10

lool

Francisco Galvan

01:15:13

1

Lily Yang

01:15:13

wait

mengzhusun

01:15:14

1

toanphan

01:15:15

1

Franklin Huang

01:15:16

1

Ethan Wu

01:15:17

1

Francisco Galvan

01:15:20

thx Jake

ayang

01:15:25

Jake poggers

Kevin Mo

01:15:32

what is the rank of the canadian flag

Ashwin Rammohan

01:15:43

3

Vainavi Viswanath

01:15:44

2?

Bryan Ngo

01:15:44

3

ayang

01:15:45

3

Stephen

01:15:45

2?

Calvin Yan

01:15:47

2

Sal

01:15:48

3?

Ethan Wu

01:15:48

2

Vainavi Viswanath

01:15:49

3

felixyu

01:15:51

3 dawg

Ayush Sharma

01:15:52

3?

Akshay Ravoor

01:15:52

3

ayang

01:15:53

yikes blue

mengzhusun

01:15:58

3

Mohsin

01:15:58

3

Sarina Sabouri

01:16:02

3

Vanshaj Singhania

01:16:04

3

Ayush Sharma

01:16:09

White/blue/white?

Lily Yang

01:16:10

4

Zhiping Gu

01:16:10

2

Stephen

01:16:11

between the white and blue horizontal

Franklin Huang

01:16:12

3

Mohsin

01:16:12

white blue white

Ranelle

01:16:25

Dang, y’all are smart. This is like an IQ test. xD

Bryan Ngo

01:16:29

red/white/blue/white/redwhite/blue/whiteblue

Sal

01:17:05

many

mjayasur

01:17:05

3

Vainavi Viswanath

01:17:07

4

ayang

01:17:07

all i see are 50 stars yeehaw

Subham Dikhit

01:17:07

Happy st pats

felixyu

01:17:08

bre

Aidan Higginbotham

01:17:09

50

Lucas Huang

01:17:10

6

mjayasur

01:17:11

A lot

Subham Dikhit

01:17:12

Cali

Alberto Checcone

01:17:13

flag stream pog

Lily Yang

01:17:14

mUrica

Bryan Ngo

01:17:20

uncountably infinite

Alberto Checcone

01:17:32

flashbacks to 70 lecture

Vanshaj Singhania

01:17:34

wait 70 isn't for another 30 minutes

Vanshaj Singhania

01:17:48

brain too fast

Bryan Ngo

01:17:54

vexillology x linear algebra

ayang

01:18:03

thats a werid variation of the hammer sickle

Subham Dikhit

01:18:04

lol

Stephen

01:18:05

its a plow?

Lily Yang

01:18:06

knowledge is deadly

Jake Whinnery

01:18:11

Looks like a ho

Francisco Galvan

01:18:12

lol

Aidan Higginbotham

01:18:13

That's a farming ho

Jake Whinnery

01:18:14

hoe*

Hamza Kamran Khawaja

01:18:15

hoe

Calvin Yan

01:18:15

Yeah hoe

Yimo Xu

01:18:17

lol

Jake Whinnery

01:18:19

Wait how do I spell it

Franklin Huang

01:18:23

great I cannot even compress the rank of this flag

ayang

01:18:24

its hoe not ho

Ranelle

01:18:29

It’s like a Vietnam, the ussr, and a euro country put together.

toanphan

01:18:42

lol

Vanshaj Singhania

01:18:44

this chat went from ee to communism real fast

Francisco Galvan

01:18:48

that was fun, A1 chat

Jake Whinnery

01:18:51

One and the same

Stephen

01:19:07

I don't think we're in Wheeler anymore

Mohsin

01:19:17

*we don’t think we’re in Wheeler anymore

Lily Yang

01:19:31

wheeler doesn't think it's wheeler anymore

Hamza Kamran Khawaja

01:19:42

there's a wheeler?

toanphan

01:20:08

There’s a zoom link to wheeler

Franklin Huang

01:20:15

wheeler is not reachable based on our current state and control parameters, we can prove it

Hamza Kamran Khawaja

01:20:22

why is wheeler??

Ranelle

01:20:27

The life of a 3rd wheeler. :’(

Stephen

01:22:07

can someone briefly explain whats the difference between outer and inner product?

James Shi

01:22:20

outer product forms a matrix

Mohsin

01:22:27

inner product maps on to a field like the real numbers

ayang

01:22:27

inner product forms a scalar

Francisco Galvan

01:22:34

inner product synonymous with dot product?

Add

01:22:35

Outer product is column x row, inner is row x column and produces one scalar value

Francisco Galvan

01:22:37

oh, yupp

Akshay Ravoor

01:22:44

Inner product of a, b is aTb but outer product is abT

Ranelle

01:22:58

Inner product is a field? Pretty sure it’s a scalar based on the mathematical definition.

Vanshaj Singhania

01:23:09

yes its a scalar

ayang

01:23:26

"In linear algebra, an inner product space is a vector space with an additional structure called an inner product. This additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors." -wikipedia

Hamza Kamran Khawaja

01:23:29

mapping onto a field means it gets one value in the field

Stephen

01:23:33

alright, thanks

Ranelle

01:24:03

But a field in algebra (linear and abstract) is a set closed under some operations.

Jake Whinnery

01:24:12

Did someone say gram Schmidt

Ranelle

01:24:26

"In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.”

Franklin Huang

01:24:30

they mean as in programming: map(list) -> number

Hamza Kamran Khawaja

01:24:32

yes, like the Real numbers which you might imagine scalars from

Bryan Ngo

01:24:44

field is some abstract algebra stuff

Franklin Huang

01:24:49

yeah

Kunaal

01:24:57

usually your field is Real/Complex

Franklin Huang

01:25:01

the abstract alg def is also true

Ranelle

01:25:41

You guys should take math 113 (abstract algebra) if time permits. That’s my all-time favorite math class!

Hamza Kamran Khawaja

01:25:59

about fields?

Ranelle

01:26:14

It’s not all fields.

Ranelle

01:26:28

You learn about fields, rings, sets, cosets, etc.

Sarina Sabouri

01:26:33

Could you repeat what the purpose of the sigmas are in the equation?

Jennifer Zhou

01:27:15

^^

ayang

01:29:11

sqrt(14)

James Shi

01:29:11

sqrt14

Sal

01:29:11

14?

Vanshaj Singhania

01:29:15

sqrt(14)

gghosal

01:29:18

sqrt(14)

Kailey

01:29:25

7

Zhiping Gu

01:29:28

sqrt(1+4+9)

Ranelle

01:29:39

14^1/2

Jennifer Zhou

01:31:35

so does the sigma basically help “make” the vectors normal, or magnitude = 1

mjayasur

01:31:51

why did we insist on length 1?

vincentwaits

01:31:55

Why do we want them to be of length1?

Ayush Sharma

01:32:47

Doesn't sigma only make the u vectors orthonormal? Why would its value depend on the v vectors - wouldn't doing that make the u vectors not normalized?

Akshay Ravoor

01:33:06

Both the u and v vectors should be orthonormal

Vanshaj Singhania

01:33:12

is that kind of like with OMP where we cared about the largest contributors? (at least I think that was OMP)

mjayasur

01:33:14

So the sigma tells us how much impact each column vector in A has on the image?

Ayush Sharma

01:33:18

AH, just saw that. Thanks @Akshay!

James Shi

01:33:29

yeah OMP seems comparable

vincentwaits

01:33:40

How do we ensure that they add up to the expected dimensions of A?

Ashwin Rammohan

01:34:04

so we're expressing the matrix A as a sort of weighted combination of other rank 1 matrices?

Vanshaj Singhania

01:34:09

looking ahead, is there a threshold for sigma for us to decide whether we care about a certain element?

Ashwin Rammohan

01:34:10

and the weights are the singular values

Ashwin Rammohan

01:34:35

@vanshaj it might be like OMP where they tell u that only 2 satellites are transmitting

Ashwin Rammohan

01:34:39

so you stop at a certain pt

Vanshaj Singhania

01:34:54

interesting. thanks!

Ashwin Rammohan

01:35:11

not sure though, maybe there is a numerical bound here. we'll see!

Hamza Kamran Khawaja

01:35:20

where is the orthogonalization part? I understand the normalization part

mjayasur

01:35:24

Do we have a way from getting to a matrix a to the SVD representation?

Lily Yang

01:35:35

m x n

vincentwaits

01:35:39

N * m

toanphan

01:35:40

Nm

James Shi

01:36:30

I think we’ll get to the algorithm for SVD later

vincentwaits

01:37:30

This is awesome

Hamza Kamran Khawaja

01:37:46

why is it r(n+m)?

dylanbrater

01:37:55

yes

Ashwin Rammohan

01:38:52

@hamza in the special case where A is rank 1, there's only one outer product so just n +m. If it's higher rank, for each number up to the rank, there's another n + m.

Ashwin Rammohan

01:38:58

So r*(n + m)

Aidan Higginbotham

01:39:42

are all of those v's transposed?

Vanshaj Singhania

01:39:53

yeah

gghosal

01:39:53

Yes

Aidan Higginbotham

01:40:00

ty

Vanshaj Singhania

01:40:35

I guess that answers my threshold question lol

Jake Whinnery

01:40:37

Why is it a reasonable assumption that sigma p is much larger than sigma p+1

Aidan Higginbotham

01:40:50

Cuz we said it was @Jakes

Vanshaj Singhania

01:40:52

i think that's an assertion @Jake

Aidan Higginbotham

01:40:54

@jake*

Lily Yang

01:40:54

we ordered them

Jake Whinnery

01:41:10

I know we ordered them but that seems like a bit of a leap in logic

Subham Dikhit

01:41:18

can't see

Subham Dikhit

01:41:37

nvm, that's the toolbar

gghosal

01:41:38

I think it happens in the real world that there are a subset of sigmas that are much larger than the rest

Franklin Huang

01:41:40

it actually happens in practice, some sigmas will have 10^-large#

gghosal

01:41:42

@Jake

ayang

01:41:44

if there is a p such that op >> op+1, then we can drop the rest of the terms after op

Ayush Sharma

01:41:57

That's what I'm thinking about too @Jake - I think perhaps an equivalent solution would be to establish some kind of "threshold" sigma where all sigma less than that are discarded. But not sure about the magnitude drop part either.

Vanshaj Singhania

01:42:25

i think the idea is that you might have some decompositions that don't have a huge impact on your image, for example

Jake Whinnery

01:42:38

Oh I guess that’s why we lose image quality in compression

Vanshaj Singhania

01:42:41

so for compression purposes you leave some off

Vanshaj Singhania

01:42:41

yeah

ayang

01:42:59

This isnt a assumption that there is always a p, its a case if this p exists

Bryan Ngo

01:43:17

are there compression algorithms in use that implement SVD

Ayush Sharma

01:43:29

Also, bumping @Hamza's earlier question - during the SVD process, where do we get to assume that the rows are orthogonal to each other?

Ayush Sharma

01:43:47

Or columns?

Sal

01:43:54

So we need to compute all p values and then sort first?

Mohsin

01:44:00

@Ayush they are orthogonal by construction

mjayasur

01:44:21

so you’re image will look worse

Hamza Kamran Khawaja

01:44:24

but that means we aren't able to do this on any matrix?

mjayasur

01:44:25

When you remake it

vincentwaits

01:45:04

Thank you

Ayush Sharma

01:45:21

OK. Thanks professors and @Mohsin! :)

Hamza Kamran Khawaja

01:45:37

so to ensure, we just construct orthogonal parts?

Jake Whinnery

01:45:54

#funWithFlags

Francisco Galvan

01:45:54

side note: I feel like im actually absorbing alot more through zoom lectures since we have to slow it down more often. :) (slow learner)

Subham Dikhit

01:45:55

heck ya, flag time

Vanshaj Singhania

01:46:03

A quick shoutout to Professor Sanders for keeping up with the chat!

Bryan Ngo

01:46:05

back to vexillology x linear algebra

Alberto Checcone

01:46:15

chin stream Pog

ayang

01:46:15

we see ur chin

Hamza Kamran Khawaja

01:46:18

@Francisco, agree

Calvin Yan

01:46:18

I second Vanshaj

gghosal

01:46:18

Not yet

Alberto Checcone

01:46:30

no it's ok this is better

Francisco Galvan

01:46:30

+1 Vanshaj

mjayasur

01:46:41

Yah esp because Professor Sanders keeps up with the chat so well everyone’s questions get answered it’s lit

Ayush Sharma

01:46:42

@Hamza I believe so - I was trying to do some different examples but couldn't convince myself that the rank vectors would always be orthogonal to each other - they'd just be linearly independent. I guess they'll talk about that later, though.

Aidan Higginbotham

01:46:46

Thank you Prof Sanders for reading the chat <3

Ayush Sharma

01:46:55

+1 +1 +1

vincentwaits

01:47:04

+ 1 Thank you Professor Sanders!

Vade

01:47:23

Prof can u zoom in

Ashwin Rammohan

01:47:26

Wouldn't a rank 1 image have every column be identical?

Ashwin Rammohan

01:47:34

it seems like the columns near the stars are still different

Terrance Li

01:47:46

^ the columns can still be scaled individually

Mohsin

01:47:47

not necessarily, they can be multiples of each other

Stephen

01:47:49

zoom in please?

Ashwin Rammohan

01:47:52

oh right

dylanbrater

01:48:16

You can just full screen

mjayasur

01:48:20

Command plus

Calvin Yan

01:48:22

Press the green button on the top right

Abhik

01:48:24

cmd plus

Vanshaj Singhania

01:48:25

cmd++

Jarvis

01:48:26

command +

Ranelle

01:48:28

And command +

Aidan Higginbotham

01:48:29

cmd plus

mjayasur

01:48:29

command plus

Francisco Galvan

01:48:30

comand+ scroll in

vincentwaits

01:48:37

Ctrl and +

Ranelle

01:48:39

Two-finger scroll

Akshay Ravoor

01:48:39

Command +

Ranelle

01:48:45

Two-finger zoom*

Akshay Ravoor

01:48:47

Pinch out with fingers

Ashwin Rammohan

01:49:15

so when he says Rank 6, he means that the estimation goes up to six rank 1 matrices right?

mjayasur

01:49:17

Lol wait the norweigan flag rank 1 is still pretty good

Ashwin Rammohan

01:49:19

so 6 singular values?

ayang

01:49:34

rank 2 has different value for the intersection of the crosses

Vanshaj Singhania

01:49:49

out of curiosity, could you put this notebook on piazza after the lecture?

Vanshaj Singhania

01:49:54

oh cool

Hamza Kamran Khawaja

01:50:02

@Ashwin, yes

felixyu

01:50:12

Do professors play video games?

Hamza Kamran Khawaja

01:50:13

6 terms of the SVD equation

Hamza Kamran Khawaja

01:50:27

@felixyu +1

Lily Yang

01:50:35

wait so the flags we saw were basically an estimation of the A matrix here right

Hamza Kamran Khawaja

01:50:46

reconstruction

Bryan Ngo

01:51:08

they were SVDs of A truncated at certain ranks

Ranelle

01:51:20

Netflix and Chill -> Zoom and Relax

ayang

01:51:21

so yes, an approximation for A

Stephen

01:51:25

spotify suggestion song sucks

ayang

01:51:30

zoom and boom actually

Jake Whinnery

01:51:38

^^^

Hamza Kamran Khawaja

01:51:45

as an aside, I love this chat

mjayasur

01:51:50

me too lol

Lily Yang

01:51:52

+1

Vanshaj Singhania

01:51:53

yeah this is kinda fun

Bryan Ngo

01:51:54

zoom emotes when

Francisco Galvan

01:51:55

netflix got rid of stars ratings after Amy Schumer

Jake Whinnery

01:52:03

Oof

Vanshaj Singhania

01:52:05

makes lecture a little more community-based

Hamza Kamran Khawaja

01:52:13

heck yea

Hamza Kamran Khawaja

01:52:18

fight the corona

Ranelle

01:52:40

You guys should watch the 20-minute Pandemic episode on Netflix.

Jake Whinnery

01:52:42

This man sounds like gru

Franklin Huang

01:52:42

star trek

vincentwaits

01:52:43

Lol

Vanshaj Singhania

01:52:43

OMG

Lily Yang

01:52:45

OMG

Ashwin Rammohan

01:52:46

LOL

Hamza Kamran Khawaja

01:52:46

YES

Lily Yang

01:52:46

NO

Francisco Galvan

01:52:46

LMAO

Vanshaj Singhania

01:52:46

IM NOT THE ONLY ONE

Lily Yang

01:52:47

A;LSKDJFSAJDLF'Q

Alberto Checcone

01:52:48

YES

Vanshaj Singhania

01:52:48

YES

Stephen

01:52:48

i can't unhear it now

ayang

01:52:48

POG CHAMP

Aidan Higginbotham

01:52:48

LOL

Sal

01:52:48

dear lord

dylanbrater

01:52:49

LOL

jeremytien

01:52:49

HAHAHAHA

Bryan Ngo

01:52:49

he's on to us

Vanshaj Singhania

01:52:49

HE DOES

Lily Yang

01:52:50

SOTOTP

Hamza Kamran Khawaja

01:52:51

LMAO

Vanshaj Singhania

01:52:53

IT'S GRU

Aidan Higginbotham

01:52:53

Prof GRU

mengzhusun

01:52:55

lmao

vincentwaits

01:52:56

HAHA

dylanbrater

01:52:57

GRUUUUU

ayang

01:52:59

PROF GRU

Hamza Kamran Khawaja

01:52:59

I WAS THINKING THE SAME THING!

Ethan Wu

01:53:06

i think boser was more Gru

Ranelle

01:53:12

LMAO

Vanshaj Singhania

01:53:26

@ethan i think prof arcak sounds more like gru in person

Subham Dikhit

01:53:27

go nick!

Franklin Huang

01:53:33

LOL no idea what their tastes are

Lily Yang

01:53:55

replace final with zoom despicable me streaming

CharlieWu

01:53:58

monkaS

Ranelle

01:53:58

Boser reminded me of the German character’s voice from zombies in Black Ops.

Bryan Ngo

01:54:24

Q1: draw a circuit diagram of vector's house

Alberto Checcone

01:54:33

in order to steal the moon, we need to use svd to compress it

ayang

01:54:41

normies

Vanshaj Singhania

01:54:48

use svd to compress the gpa requirement

Ayush Sharma

01:54:50

For real though, @staff, may we have a Despicable Me-themed final question? :)

Vanshaj Singhania

01:55:54

can we extra credit for compressing despicable me

Ashwin Rammohan

01:56:30

so sigma here would be how important brightness is compared to other factors?

Akshay Ravoor

01:56:50

correct

Franklin Huang

01:56:54

*a disentanglement problem is slowly bubbling up to the surface*

vincentwaits

01:57:45

YES PLS

felixyu

01:57:48

😣

Vanshaj Singhania

01:57:49

yesss

Hamza Kamran Khawaja

01:57:53

but for separate movies, brightness for comedy, for action etc

Ashwin Rammohan

01:57:53

this is rly cool

Ranelle

01:57:57

Alright, see you Thursday, class! It was fun learning and chatting!

Francisco Galvan

01:57:57

THANK YOU PROFESSORS, the both of you guys!

Stephen

01:57:59

thank u

vincentwaits

01:58:00

THANK YOU!!!

Jennifer Zhou

01:58:02

Thank you!!!!

Ashwin Rammohan

01:58:02

thank you

Vanshaj Singhania

01:58:02

thank you guyssss

Lily Yang

01:58:03

THANKS

Ayush Sharma

01:58:03

Thank you! :D

Franklin Huang

01:58:04

thank you!

Hamza Kamran Khawaja

01:58:04

GREAT LECTUER

Jamie

01:58:06

thank you!

dylanbrater

01:58:06

thx

Hamza Kamran Khawaja

01:58:06

LECTURE

Abhik

01:58:08

thank you!

Sal

01:58:09

this was such a good lecture

ayang

01:58:12

ty prof gru

Ranelle

01:58:12

Muchas gracias, profesores!

Calvin Yan

01:58:14

No questions. Thanks so much!

Evelyn Pinjen Wu

01:58:15

Thank you!

Kunaal

01:58:15

thank you

felixyu

01:58:16

Do profs play video games? @seth

Jiachen Yuan

01:58:18

thx

Helen Peng

01:58:20

thank you!!!!!

Alberto Checcone

01:58:22

can we have more chin streams

Sarina Sabouri

01:58:23

Thank you so much!

Aidan Higginbotham

01:58:23

Thank you!

vincentwaits

01:58:23

You too Professor Seth!

Vanshaj Singhania

01:58:25

can we add you guys on discord

Francisco Galvan

01:58:26

100/1000+ students curr attending

Jiachen Yuan

01:58:26

really cool examples!

Add

01:58:29

Thanks!

Jenny

01:58:31

discorddd

Francisco Galvan

01:58:31

lol

vincentwaits

01:58:32

:)

Lily Yang

01:58:32

:))))))

Jessie Siyi Ren

01:58:33

Very clear, thanks!