My Understanding of the Manifold Hypothesis - structure in real world data - Generative Modeling
ฝัง
- เผยแพร่เมื่อ 29 มี.ค. 2020
- If you think I've misunderstood something, please let me know in the comments!
Below is the mash up of quotes which motivate this video:
Real datasets actually contain a tremendous amount of structure, or else we could not learn from them. The manifold hypothesis is that real life high-dimensional data of interest often
lives in an unknown lower-dimensional manifold embedded in ambient space.
it is only slightly overstating the case to say that physics is the study of symmetry.
Below are all the blogs/papers/videos I've referred to:
Blogs:
en.wikipedia.org/wiki/Hypercube
computervisionblog.wordpress....
computervisionblog.wordpress....
prateekvjoshi.com/2014/06/21/...
/ a-journey-through-mult...
colah.github.io/posts/2014-03-...
bjlkeng.github.io/posts/manifo...
Lectures:
• Lecture 2/16 : The Per...
• From Deep Learning of ...
videolectures.net/mlss09us_niy...
videolectures.net/deeplearning...
Papers:
openaccess.thecvf.com/content_...
openscholarship.wustl.edu/cgi/...
arxiv.org/abs/1609.03552
www.lcayton.com/resexam.pdf
Videos and GAN implementations:
• Chairs morphing
• The 1000 ImageNet Cate...
• InterFaceGAN Demo (CVP...
• Video
• Stylegan on Anime Girls
__________________________________________________
Social Media:
Kartik Chincholikar Website: kartikchincholikar.github.io/
Github: github.com/kartikchincholikar
Twitter: / kartikc14
_______________________________________________
I love coffee! Help fund future projects:
www.buymeacoffee.com/karti
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Music:
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Free Download / Stream: bit.ly/2vkP2eN
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I rarely comment on videos, but I felt that I needed to let you know: This is pedagogically beautiful. Very well done. Please don't let this be the last of this kind of videos.
Thank you for your kind words :)
Yes
I agree. I subscribed. Thank you for sharing
This video represents the point on the educational manifold where a smile appears. Thanks for taking us there.
Hahahaha thanks!
As a PhD doing work in this field. Man, this was refreshing. Really great work, keep it up my man!
I have searched lots of manifold related videos on TH-cam, and this is the one that I feel the best!
Thank you ! :)
I totally agree
The elegance of this explanation is breathtaking!
Only 30k views. This video deserves more, makes it visually easy for anyone to get a better grasp of what a manifold is.
Thank you! 🙏
Wow i feel like i have had an illumination about how Ai work in general, thank you
I'm a newbie in this field & I must tell you this is the most amazing ML video I've seen until now. Thank u so much!
Sad that youtube havent find a better manifold to recommend this 2021
Amazing video, a classic 😎
Thank you!! This means a lot!
Wonderfully intuitive video. Thank you for making it
Thank you Kartik for making such an intuitive video! Cheers!
One of the best explanations. The « mapping » part towards the end was particularly useful for me.
I clicked on this because it was randomly recommended to me. I had no idea what the word "Manifold" even meant, and after just six and a half minutes I have a really good general understanding and starting point to continue looking into this interesting topic. Amazing video!
My favourite part of the video? The description. Unlike a certain charlatan who says "learn X in five minutes" and acts as if he came up with everything, I like your under-stated / non-flashy way of presenting as well as giving total credit to all the papers/code involved.
thanks :)
Masterfully done. Thank you 🙏🏾
Excellent!! I am speechless by the simplicity of this video and the amount of information it conveyed under 7 minutes
Thanks 🙏
Thank you for this - very clear and informative.
Additionally, we know that the clock manifold must be homomorphic to SO2, since after 12 hours you will get the same image again.
Which let's us know - by topology - why the linear interpolation in the ambient space (on some image pairs) does not work: it has a hole.
This is true only for a a particular clock with a frame fixed in the image. What is true however is that the clock manifold would be a principal SO(2) bundle, meaning that there is a base space of clocks, say with any clock, spacially fixed in the frame, having time exactly 12:00, and then the SO(2) fibre is that of the hands spinning around until it is 12:00 again.
@@chasebender7473 Yes that's true, the actual manifold (for all clocks and all positions) is much more complex.
But I wounder why you would choose a particular time for the base space?
Since SO2 has no prefered orientation, I would think of the base space as a cross product of all possible clocks - fixed in the frame without any fingers - times all possible fingers without any orientation.
Important insight !👍
I have legit not found a better explanation of the manifold hypothesis till now. I am trying to teach myself about smooth manifolds and algebraic topology, and some real-world intuition/background to topics always helps. So yeah, can't thank you enough for the video, mayte!
This is an amazing video. I am a data scientist for a company. Best explanation I've heard in a long time.
Well, this video is just beautiful. Hope the algorithm blesses more people with finding about it
I stumbled on to this video, but this is the explanation of manifolds that I had been searching for ages. Thank you so much!
Thank you :)
One more comment to express how you have summarized me a day of research on those learning. Amazing teaching skills. Please continue doing what you are talented at: explaining simply complex notions !
Thank you !
Brilliantly explained, make more please!
yup, on it!
Well explained like crystal clear. You shuold continue doing these types of videos. They are inspiring concepts of ai field.
Thank you very much!
Just saw your comment. Great work on getting started! Phenomenal production value here. Subbed.
Thank you!
This is simply excellent.
Extremely awesome. Clear and Concise. @3Blue1Brown will be so proud of you :)
The part about how staying on the manifold visualizes faces and going off it gives an abrupt transition is the most intuitive explanation of manifold that I've ever seen. Safe to say, your explanation blew my face off ;)
I feel like I'll carry this sequence in my brain when I visualize a manifold. Kudos to you on creating this video, please don't stop creating such videos. ML space needs more of such videos.
This is incredibly well presented. Thank you. Amazing work 🙏
A great teacher can be recognized by the ability to present information in such way, that even an absolute amateur is able to comprehend the basic concepts. And from an amateurs point of view, this is definitely the case with you. 🙏
Interesting video and well illustrated explanation
So much better than the 'Wikipedia' [pure mathematician] approach. Insightful. I'd seen the words and sort of had a slippery handhold on the terms but this gave a level of 'concreteness' to allow the abstractness to be seen (skeletons as naked humans ;-)
This is incredible, thank you so much
Excellent! I was stuck in thinking of wavy manifolds but it never occurred to me it can be done via hypercube.
That was one of the best educational videos I have seen on a subject of machine learning!
Really awesome is the feeling of unserstanding math
Whenever I try to understand manifold, somehow I brain gets folded and twisted to achieve of some sort of manifold.
Well, this video helped me to make the folded brain straight. 🙂
Thank you sir! You helped me make the association between linear regression and deep learning! deep learning generalizes patterns of high dimensional data to a manifold just like linear regression generalizes patterns of two dimensional data into a line! Thank you!
Bro you have absolutely deep taste about math understanding awesome vid
Wow! This was incredible. You should be really proud of this description of such a complex topic.
Top notch video, brotherman.
Very well done. It's great instructional material as the ideas behind the manifold hypothesis can often be muddied by complex equations and a lack of helpful visualisations. Your video gives an excellent overview.
Incredible stuff with an elucidating explanation! Subscribed in hopes there might be more to come
That was the clearest explanation of this topic of manifolds and latent space I have ever come across. Excellent!
This is so freaking cool. Thank you for the great video.
Amazingly clear video! Please make more!!
Very good video, Thanks!
What a great explanation!
Fantastic explanation on the intuition behind this. Great work
Wow man this is very informative and beautiful! I was studying the adversarial examples paradox and came across your video and it helped me a lot! Thank you and keep up the good work!
This one is so good, thank you for producing it!
Bro, this is sooooo underrated.... Like the production value is too good. And the laid-back humble vibe you give off is awesome! Continue to make more!
Well that was a fun and beautiful explanation! I hope you make more videos, you explain very well.
Awesome video! This makes me actually want to read more about it instead of feeling like I have to because of my class
The concept was articulated really well. Thank you 😊
thanks for the video, u made the concept look so simple
Great video, probably the best manifold hypothesis explanation I have seen around. Keep up the good content.
beautifully done.
Sooooo well done! II understand manifolds so, so much better now. Thank you!
This is absolutely fascinating and so well made!
thanks!
very few concepts reshape my conception of reality but this one is one of them. Thanks bro.
We're all just on a super high dimensional manifold. Who's to say our dx experience of the whole manifold is representative even slightly of any random point on our manifold (reality)
Thank you for your kind words!
Amazing video! Keep it up!
Great work Kartik!! This is truly a beautiful illustration of how manifolds can be imagined in ML!
Thank you for sharing your understanding of the manifold hypothesis. This really helped in visualising the mapping and the mathematics in many papers.
:)
This is the best explanation about manifold so far! Great job dude, keep going
Thank you!
This is a super strong and well-made bit of exposition. Well done!
Amazing explanation! Thank you so much for this 😊
Beautifully explained and visualized, great work brother🔥
You just became one of my favourite youtubers.
Fantastic, elegant explanation. Please don't stop making these!
Thanks! I do plan on making more videos :)
incredible explanation
Really Amazing to watch...
Holy moly, this was fantastic. Please keep these videos coming! Very impressively clear explanation and succinct exploration of the topic. Beautiful done!
Thank you! 😄
More power to you buddy! Expecting more videos like this
This is great. Hope you make more.
Loved the video, soo lovely.
This video gave me chills. Excellently done, thank you Kartik!
Thanks!
This is fantastic! Beautifully explained!
thanks bro
This is an excellent illustration!
This is fantastic ! Thank you.
Amazing work bro
Seriously excellent work. Thank you for putting this together.
Also, who was the quote about visualizing the R^14 hypercube from? :D
thanks! The quote is by Geoffrey Hinton, and is taken from this lecture:
th-cam.com/video/TNhgCkYDc8M/w-d-xo.html
Very well done! Thanks for your video!
Easily one of the best machine learning videos I've ever seen. Please make many more.
Thank you :) I will!
Well explained and really good production!
Thanks!
Fantastic video! Keep up the great work. :)
Thanks! :)
your work is amazing , waiting for more videos.
Thank you Jinny😂🙊
Thank you. This helped me.
very good video, thank you
thank you for making the video!! I learned a lot
OMG! This is amazing! Thank you
Awesome! Easy to understand and well explained, good job Kartik 😊👍
Thanks!!
this video is a hidden gem!
great video, thanks a lot!
Nice job! Thanks for making the video.
Thanks!
10/10 need more
As clear as crystal. Great video!
thank you!
Beautiful explanation! Waiting for more videos on linear algebra and dimensions.
thanks 😁!
Thank you for a great explanation :)
This video is amazing, thank you