My Understanding of the Manifold Hypothesis - structure in real world data - Generative Modeling

[@mohammedal-jaff617]

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.

[@Kartik_C]

Thank you for your kind words :)

[@spiralofinspiration3653]

Yes I agree. I subscribed. Thank you for sharing

[@genecat]

This video represents the point on the educational manifold where a smile appears. Thanks for taking us there.

[@Kartik_C]

Hahahaha thanks!

[@NinadMehta]

Only 30k views. This video deserves more, makes it visually easy for anyone to get a better grasp of what a manifold is.

[@Kartik_C]

Thank you! 🙏

[@DeepakSingh-ji3zo]

Excellent!! I am speechless by the simplicity of this video and the amount of information it conveyed under 7 minutes

[@Kartik_C]

Thanks 🙏

[@Yavanna16]

The elegance of this explanation is breathtaking!

[@Arthurein]

As a PhD doing work in this field. Man, this was refreshing. Really great work, keep it up my man!

[@robelle1357]

I have searched lots of manifold related videos on KZbin, and this is the one that I feel the best!

[@Kartik_C]

Thank you ! :)

[@Jofferpg2009]

I totally agree

[@tomoki-v6o]

Sad that youtube havent find a better manifold to recommend this 2021

[@gorkemgumusboga3717]

Well explained like crystal clear. You shuold continue doing these types of videos. They are inspiring concepts of ai field.

[@Kartik_C]

Thank you very much!

[@cafardine]

One of the best explanations. The « mapping » part towards the end was particularly useful for me.

[@shilparani9080]

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!

[@Chev29]

Wow i feel like i have had an illumination about how Ai work in general, thank you

[@zeldaau1017]

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!

[@alioraqsa]

This is the best explanation about manifold so far! Great job dude, keep going

[@Kartik_C]

Thank you!

[@gregorycowan8215]

Wonderfully intuitive video. Thank you for making it

[@joshuaclancy8093]

Brilliantly explained, make more please!

[@Kartik_C]

yup, on it!

[@venugopalmani2739]

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.

[@Kartik_C]

thanks :)

[@sayrun75]

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 !

[@Kartik_C]

Thank you !

[@advaitathreya5558]

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.

[@RyanMcCoppin]

This is an amazing video. I am a data scientist for a company. Best explanation I've heard in a long time.

[@vishalagarwal4766]

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!

[@drsoumyabanerjee]

I stumbled on to this video, but this is the explanation of manifolds that I had been searching for ages. Thank you so much!

[@Kartik_C]

Thank you :)

[@MachineLearningStreetTalk]

Amazing video, a classic 😎

[@Kartik_C]

Thank you!! This means a lot!

[@MachineLearningwithPhil]

Just saw your comment. Great work on getting started! Phenomenal production value here. Subbed.

[@Kartik_C]

Thank you!

[@JensDoll]

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.

[@chasebender7473]

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.

[@JensDoll]

@@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.

[@mrtertg2603]

Important insight !👍

[@nichy777]

Wow! This was incredible. You should be really proud of this description of such a complex topic.

[@Silvannetwork]

Interesting video and well illustrated explanation

[@jmchdjaimerporkpuedolol3681]

Well, this video is just beautiful. Hope the algorithm blesses more people with finding about it

[@martinmazanek5192]

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. 🙏

[@arsenbaiken4345]

That was one of the best educational videos I have seen on a subject of machine learning!

[@gluteusminimus2134]

Great video, probably the best manifold hypothesis explanation I have seen around. Keep up the good content.

[@samuraijosh1595]

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!

[@sudarshangurung7500]

Bro you have absolutely deep taste about math understanding awesome vid

[@juliocardenas4485]

Masterfully done. Thank you 🙏🏾

[@tylertheeverlasting]

This is simply excellent.

[@daanishrizvi]

Great work Kartik!! This is truly a beautiful illustration of how manifolds can be imagined in ML!

[@jeremyfmoses]

Thank you for this - very clear and informative.

[@SundaralingamS]

Extremely awesome. Clear and Concise. @3Blue1Brown will be so proud of you :)

[@gergerger53]

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.

[@DougMayhew-ds3ug]

That was the clearest explanation of this topic of manifolds and latent space I have ever come across. Excellent!

[@nextwave319]

Excellent! I was stuck in thinking of wavy manifolds but it never occurred to me it can be done via hypercube.

[@zahid1909]

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. 🙂

[@SamirPatnaik]

Top notch video, brotherman.

[@grahzac]

Well that was a fun and beautiful explanation! I hope you make more videos, you explain very well.

[@FreeMarketSwine]

Easily one of the best machine learning videos I've ever seen. Please make many more.

[@Kartik_C]

Thank you :) I will!

[@mayurdhande2453]

Thank you Kartik for making such an intuitive video! Cheers!

[@siddhantrai7529]

Beautifully explained and visualized, great work brother🔥

[@zsolt-balla]

You just became one of my favourite youtubers. Fantastic, elegant explanation. Please don't stop making these!

[@Kartik_C]

Thanks! I do plan on making more videos :)

[@zherao5554]

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!

[@prabhavkaula9697]

Thank you for sharing your understanding of the manifold hypothesis. This really helped in visualising the mapping and the mathematics in many papers. :)

[@RoobertFlynn]

What a great explanation!

[@thechhavibansal]

thanks for the video, u made the concept look so simple

[@andybrice2711]

This is an excellent illustration!

[@krystalp9856]

Awesome video! This makes me actually want to read more about it instead of feeling like I have to because of my class

[@elblanco5]

Holy moly, this was fantastic. Please keep these videos coming! Very impressively clear explanation and succinct exploration of the topic. Beautiful done!

[@Kartik_C]

Thank you! 😄

[@oliverclive-griffin3454]

This is incredible, thank you so much

[@chemicalengineeringfriends217]

The concept was articulated really well. Thank you 😊

[@deltax7159]

beautifully done.

[@sksridhar1018]

Fantastic explanation on the intuition behind this. Great work

[@philipoakley5498]

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 ;-)

[@sudarshangurung7500]

Really awesome is the feeling of unserstanding math

[@TheDRAGONFLITE]

This is so freaking cool. Thank you for the great video.

[@archamondearchenwold8084]

Sooooo well done! II understand manifolds so, so much better now. Thank you!

[@AnilKeshwani]

This is a super strong and well-made bit of exposition. Well done!

[@sonalitungare5644]

Awesome! Easy to understand and well explained, good job Kartik 😊👍

[@Kartik_C]

Thanks!!

[@noahgsolomon]

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)

[@Kartik_C]

Thank you for your kind words!

[@chroozen]

This video gave me chills. Excellently done, thank you Kartik!

[@Kartik_C]

Thanks!

[@dudewaldo4]

Incredible stuff with an elucidating explanation! Subscribed in hopes there might be more to come

[@tristanwegner]

Good explanation style

[@tinkeringengr]

Amazingly clear video! Please make more!!

[@xhinker]

Very good video, Thanks!

[@belalmatter256]

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!

[@Booze8D]

Amazing video! Keep it up!

[@The98Ringo]

I've been reading Deep Learning with Python by Francois Chollet (great book for beginners to Deep Learning btw.) He explains everything very clearly, but I was really struggling with a subchapter called manifold hypothesis. After watching this video I really start to understand what he was trying to say. Thank you very much for your input. Great work!

[@Kartik_C]

thank you! Do check out the references in the description if you wish to learn more :)

[@josevalverde5066]

incredible explanation

[@ahmaddraza]

Amazing work bro

[@adamtaylor2142]

Seriously excellent work. Thank you for putting this together.

[@adamtaylor2142]

Also, who was the quote about visualizing the R^14 hypercube from? :D

[@Kartik_C]

thanks! The quote is by Geoffrey Hinton, and is taken from this lecture: kzbin.info/www/bejne/in_LmHahjqmWbq8

[@prettiestthing]

Amazing explanation! Thank you so much for this 😊

[@AdobadoFantastico]

This is great. Hope you make more.

[@brownbadass8316]

This gave me a better understanding of GANs. Loved your work

[@Kartik_C]

Thank you :)

[@kaushikgupta1410]

Really Amazing to watch...

[@vvortex2931]

This one is so good, thank you for producing it!

[@rohitmujumdar8195]

This is absolutely fascinating and so well made!

[@Kartik_C]

thanks!

[@mahmoudbakr568]

Loved the video, soo lovely.

[@ChrisOffner]

Fantastic video! Keep up the great work. :)

[@Kartik_C]

Thanks! :)

[@adelarscheidt]

That was very insightful and easy to follow

[@adelarscheidt]

I have a question though. Is the manifold locally flat or does it have thickness?

[@Kartik_C]

Thanks! I don't know the answer to this question. I think of it as a (relatively) low dimensional cloud ( or probability distribution ) in the hypercube. A face is still going be a face if we slightly move in any direction . Disclaimer: As everything is in high dimensions, even this intuition is probably wrong..

[@UdemmyUdemmy]

If tasked with explaining an astrophysics concept I think you would make a good explanation on that too though

[@fenglongsong4760]

Very well done! Thanks for your video!

[@Anki_jinny]

your work is amazing , waiting for more videos.

[@Kartik_C]

Thank you Jinny😂🙊

[@AIwithHasanAliNaqvi]

More power to you buddy! Expecting more videos like this

[@zg7860]

very good video, thank you

[@openroomxyz]

This is amazing thanks for creating this beautiful video

[@Kartik_C]

Thanks!

[@moegreen7023]

Thank you. This helped me.

[@joseph3543]

great video, thanks a lot!

[@MargaretSpintz]

this video is a hidden gem!

[@gingerprince2062]

10/10 need more

[@DevanshKhandekar]

Wonderful Kartik. So all the latent features can be interpreted as the interpolated features of the original features with exactly the same degrees of freedom? It will be exciting to explore the research areas where the focus is to traverse along different paths, experimenting with. different degrees of freedom. This will have greater impact in the audio generation fields. Thank you for this explanation. So apt and very well explained with visualizations. I'd really love to see some more content like this.

[@sudarshangurung7500]

Waah achhxa laga kartik

[@pobttt8925]

great video

[@zuggrr]

This is fantastic ! Thank you.