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.
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.
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!
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.
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 !
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!
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.
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!
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.
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!
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 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. 🙏
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!
Holy moly, this was fantastic. Please keep these videos coming! Very impressively clear explanation and succinct exploration of the topic. Beautiful done!
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)
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. 🙂
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!
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.
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 great. Is there a way for an MLA to estimate precisely a point on the manifold with small datasets, perhaps with some prior training, or training on data which is somewhat associated, but not directly related to the x-manifold it is searching for?
I wanted to say thank you for including the clock manifold! It’s got me started down a rabbit hole thinking about the relationship between time and our universe, and what shape worldlines might take. Are our 3 spatial dimensions and 1 temporal dimension the intrinsic dimensions of an embedded manifold? Are there any techniques for determining the embedding dimensions for a space while only knowing the intrinsic dimensions of the manifold inside, and can we use that methodology to determine with any level of certainty whether our own universe is embedded within higher dimensions (and what those are)? If manifolds are subsets of a space that describe the set of points possible under given conditions/laws (constraints), can those laws be derived from the manifold if it is constructed from data rather than calculated using laws? Could we gain a better understanding of gravity this way? I have bills to pay and no high-level scientific education so hopefully the answers are out there, or someone’s working on them.
These are very interesting questions! What I've covered here is just the tip of the iceberg. I think you would dig these two lectures: 1)ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-pkJkHB_c3nA.html 2)ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-w6Pw4MOzMuo.html
