Dear Fellow Scholars, this is Two Minute Papers

with Károly Zsolnai-Fehér. This piece of work is not meant to be a highly

useful application, only a tongue in cheek jab at the rising trend of trying to solve

simple problems using deep learning without carefully examining the problem at hand. As always, we note that all intuitive explanations

are wrong, but some are helpful, and the most precise way to express these thoughts can

be done by using mathematics. However, we shall leave that to the textbooks

and will try to understand these concepts by floating about on the wings of intuition. In mathematics, a matrix is a rectangular

array in which we can store numbers and symbols. Matrices can be interpreted in many ways,

for instance, we can think of them as transformations. Multiplying a matrix with a vector means applying

this transform to the vector, such as scaling, rotation or shearing. The rank of a matrix can be intuitively explained

in many ways. My favorite intuition is that the rank encodes

the information content of the matrix. For instance, in an earlier work on Separable

Subsurface Scattering, we recognized that many of these matrices that encode light scattering

inside translucent materials, are of relatively low rank. This means that the information within is

highly structured and it is not random noise. And from this low rank property follows that

we can compress and represent this phenomenon using simpler data structures, leading to

an extremely efficient algorithm to simulate light scattering within our skin. However, the main point is that finding out

the rank of a large matrix is an expensive operation. It is also important to note that we can also

visualize these matrices by mapping the numbers within to different colors. As a fun sidenote, the paper finds, that the

uglier the colorscheme is, the better suited it is for learning. This way, after computing the ranks of many

matrices, we can create a lot of input images and output ranks for the neural network to

learn on. After that, the goal is that we feed in an

unknown matrix in the form of an image, and the network would have to guess what the rank

is. It is almost like having an expert scientist

unleash his intuition on such a matrix, much like a fun guessing game for intoxicated mathematicians. And the ultimate question, as always is, how

does this knowledge learned by the neural network generalize? The results are decent, but not spectacular,

but they also offer some insights as to which matrices have surprising ranks. We can also try computing the products of

matrices, which intuitively translates to guessing the result after we have done one

transformation after the other. Like the output of scaling after a rotation

operation. They also tried to compute the inverse of

matrices, for which the intuition can be undoing the transformation. If it is a rotation to a given direction,

the inverse would be rotating back the exact same amount, or if we scaled something up,

then scaling it back down would be its inverse. Of course, these are not the only operations

that we can do with matrices, we only used these for the sake of demonstration. The lead author states on his website that

this paper shows that “linear algebra can be replaced with machine learning”. Talk about being funny and tongue in cheek. Also, I have linked the website of David in

the description box, he has a lot of great works and I am surely not doing him justice

by of all those great works, covering this one. Rufus von Woofles, graduate of the prestigious

Muddy Paws University was the third author of the paper, overlooking the entirety of

the work and making sure that the quality of the results is impeccable. As future work, I would propose replacing

the basic mathematical operators such as addition and multiplication by machine learning. Except that it is already done and is hilariously

fun, and it even supports division by zero. Talk about the almighty powers of deep learning. Thanks for watching, and for your generous

support, and I’ll see you next time!

Was this episode understandable? Were there terms that were not explained clearly? Or was everything fine in there? Let us know, we love to read your feedback! 🙂

<Personal Opinion>This is typically a domain where the Deep-Learning should not be used ( :</Personal Opinion>

We understand enough matrices why do we want an approximative result where the exact one exist?

<Objection of the Personal Opinion>Exception of my senstence: When we want fast approximative result, I should test it on large matrix 10^5; 10^6 before to claim that :D</Objection of the Personal Opinion>

LMAO. Wassup Karo? You good?

Haha, that was great!

I'm glad that you went a little more in-depth this time around. Ironically enough, you did that for a joke-paper.

I think this is closer to what this channel should be than the last couple videos. – For me this was still too light to really learn something new (I know linear algebra and am familiar with ranks) but that's probably not necessarily the case for the majority of watchers.

Karoly, I love your channel so far and look forward to every video. Have you heard about the recent paper "Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network"? The results are absolutely mind-blowing, and the 4x downscaled then upscaled image looks nearly indistinguishable from the original image. I know some people look down on anything that uses a GAN, but I think the results speak for themselves. I'm guessing you already saw it on /r/machinelearning, but here it is if you haven't seen it yet: http://arxiv.org/abs/1609.04802

can we make old black white movies colorfull with machine learning?

In the video, you're showing the web interface, which (if I understand correctly) can't use machine learning (that's why it says "real"). So you're just showing an ordinary calculator. You have to download and build the electron app to use the learned operations.

However, I was unable to get anything but "real" mode to work by just following the readme. The "=" button seemed to just have no effect. A shame, because it's a really cute idea.

I lold. I am myself trying to train a deep neural network on videos of me working so that I can take the day off, courtesy of machine learning.

HAHAHHA de gaulle !

But why? XD It feels like calculating the rang of a matrix would be one of the last things that you would be able to teach a neural network.

de gaulle lol! BTW, I like this application of NNs!

OMG, this is awesome 🙂

Your videos are always entertaining and full of great things

Dich hat schon immer interessiert, wie machine learning funktioniert?