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Convexity and The Principle of Duality

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Visually Explained

Visually Explained

Күн бұрын

Пікірлер: 76
@snailscout9383
@snailscout9383 Жыл бұрын
I feel fortunate to live in a time were there are people who teach hard-to-understand concepts for free in a easy to grasp fashion. Hats off to you and thank you a lot
@hyperduality2838
@hyperduality2838 Жыл бұрын
From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law of thermodynamics all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Teleological physics (syntropy) is dual to non teleological physics (entropy). Duality creates reality. "Always two there are" -- Yoda. Points are dual to lines -- the principle of duality in geometry.
@jiaqi9113
@jiaqi9113 3 жыл бұрын
Extremely good introduction!!!! It is very hard to imagine how much work put behind the video!! Thanks for your input on this!! I already worked on convex optimization problem in a research project for a few months but honestly I really don't know what is special about convex optimization. Thanks for giving us the intuition behind it!!
@hyperduality2838
@hyperduality2838 Жыл бұрын
From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law of thermodynamics all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Teleological physics (syntropy) is dual to non teleological physics (entropy). Duality creates reality. "Always two there are" -- Yoda. Points are dual to lines -- the principle of duality in geometry.
@raulsena3917
@raulsena3917 2 жыл бұрын
Thanks for the video, I was reading many books to understand this and you explain it plain and simple. Keep it up!
@virmaq5187
@virmaq5187 2 жыл бұрын
As a visual learner, this video helped me tremendously. Thank you!
@parahumour4619
@parahumour4619 8 ай бұрын
Amazing video, your channel deserves more views. I would suggest having a section where you ask the viewers questions so they stop and think and end up being onboard with the understanding
@vats6
@vats6 2 жыл бұрын
Woah! Thanks a lot sir, for such an intutive explaination of convexity. The best explaination I have seen on the internet so far!
@hyperduality2838
@hyperduality2838 Жыл бұрын
From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law of thermodynamics all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Teleological physics (syntropy) is dual to non teleological physics (entropy). Duality creates reality. "Always two there are" -- Yoda. Points are dual to lines -- the principle of duality in geometry.
@cmatiolli13
@cmatiolli13 Жыл бұрын
Your videos are awesome. The right balance of math concepts and intuition to explain complex ideas is the perfect fit for this essential concept.
@hyperduality2838
@hyperduality2838 Жыл бұрын
From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law of thermodynamics all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Teleological physics (syntropy) is dual to non teleological physics (entropy). Duality creates reality. "Always two there are" -- Yoda. Points are dual to lines -- the principle of duality in geometry.
@imotvoksim
@imotvoksim 2 жыл бұрын
The least squares example you show at 7:59 has a wrong sign as far as I can tell!.Otherwise a great video providing the intuition I was looking for, took down some notes, hopefully they finally stick and I understand this dual magic once and for all, thanks!
@VisuallyExplained
@VisuallyExplained 2 жыл бұрын
You are correct about the wrong minus sign, thanks for watching the video carefully, and thank you for the very nice comment. I am glad the video was helpful to you. :-)
@wexwexexort
@wexwexexort 11 ай бұрын
I always like to watch the visual explanations even though I know the topic quite well and to be honest, you do a really good job on both explanations and visuals.
@Sirentuber
@Sirentuber Жыл бұрын
Good God. This is so beautiful and intuitively explained. Can thank you enough for this! you are the savior.
@colin_hart
@colin_hart 2 жыл бұрын
The code samples for linear programming and least squares are swapped at 0:23. I’ve been enjoying your work. Thanks for sharing!
@VisuallyExplained
@VisuallyExplained 2 жыл бұрын
Thanks for watching carefully, and I am glad you liked my videos. :-)
@rubenosmond8200
@rubenosmond8200 10 ай бұрын
Thank you sir. I'm having a hard time understanding this concept for my machine learning class and you helped me in a beautiful fashion. May you have great things in line.
@SonLeTyP9496
@SonLeTyP9496 3 жыл бұрын
Awesome :) cant wait to see next episode :D
@think9824
@think9824 3 жыл бұрын
true
@MaxWasserman1
@MaxWasserman1 3 жыл бұрын
Huge fan. Keep it up.
@gustavgille9323
@gustavgille9323 2 ай бұрын
The least squares error example is beautiful!!!
@ian.ambrose
@ian.ambrose Жыл бұрын
Yes! New Blender tutorial!
@nashwahammoud4076
@nashwahammoud4076 5 ай бұрын
That's wonderful 🎉 thanks for you
@jiaqint961
@jiaqint961 Жыл бұрын
I learnt so much from this video, I love you so much
@phogbinh
@phogbinh 2 жыл бұрын
God like overview of the topic. Thank you.
@user-nm3mn1ir2z
@user-nm3mn1ir2z Жыл бұрын
great video! What program did you use to make this fantastic visualization?
@ZhanCaitao
@ZhanCaitao 2 жыл бұрын
Great video!
@lilialola123
@lilialola123 Жыл бұрын
AMAZING visualizations, thank you
@parhamzolfaghari7394
@parhamzolfaghari7394 10 ай бұрын
Wonderful! I always wonder why the professors and teacher follow the worst method possible to teach materials.
@jameskirkham5019
@jameskirkham5019 3 ай бұрын
Amazing video thank you
@thebifrostbridge3900
@thebifrostbridge3900 2 жыл бұрын
Great video. Fun fact, the autogenerated subtitles at 9:32 says: "to optimization problems with cancer friends"
@chinmaydhole4001
@chinmaydhole4001 2 жыл бұрын
mind blown! thanks a lot for this video
@mandystritzke3339
@mandystritzke3339 3 жыл бұрын
Great explanation!
@jsalca52
@jsalca52 3 жыл бұрын
Shokran kathir!
@think9824
@think9824 3 жыл бұрын
very interesting and useful. thanks a lot
@LuisLascanoValarezo
@LuisLascanoValarezo Жыл бұрын
7:59 Formula is key for interviews and in Machine Learning
@_soundwave_
@_soundwave_ 10 ай бұрын
What about convex in terms of geometry? What about all three definition of convexity with that of geometry?
@AJ-et3vf
@AJ-et3vf Жыл бұрын
awesome video. thank you
@fabricetshinangi5042
@fabricetshinangi5042 2 жыл бұрын
Amazing video, thank you for the explanation
@VisuallyExplained
@VisuallyExplained 2 жыл бұрын
Glad it was helpful!
@fabricetshinangi5042
@fabricetshinangi5042 2 жыл бұрын
Yes it is very insightful. I'm actually optimizing a Non linear cost function (with more than 6 variables) using newton raphson method. And my hessian matrix must be >=0
@federicobarra3655
@federicobarra3655 2 жыл бұрын
amazing explanation! keep it up!
@VivekYadav-ds8oz
@VivekYadav-ds8oz 5 ай бұрын
I don't get how h(x)
@VisuallyExplained
@VisuallyExplained 4 ай бұрын
-e^x is not convex
@sateeshk3347
@sateeshk3347 2 жыл бұрын
Great Video, thank you for the effort and time in creating the same.
@VisuallyExplained
@VisuallyExplained 2 жыл бұрын
My pleasure!
@werdasize
@werdasize 2 жыл бұрын
Really nice! But one thing I didn’t understand was at 5:02 ish. You say that the intersection of those support planes is the convex set.. but in your example, isn’t the intersection of the planes just a bunch of connected lines? Not sure if I understood correctly.
@werdasize
@werdasize 2 жыл бұрын
Or is it that there exists an infinite set of unique such planes whose intersection is the surface of the convex set? Even then, still not sure how to recover the interior.
@VisuallyExplained
@VisuallyExplained 2 жыл бұрын
Great observation. The intersection of the hyperplanes themselves could be empty. It is the intersection of the corresponding half spaces that gives the convex set.
@werdasize
@werdasize 2 жыл бұрын
@@VisuallyExplained makes perfect sense then, thanks!!
@tomwassing
@tomwassing 3 жыл бұрын
Absolutely amazing video! Great visualisation and explanation of the topic. I found it pretty difficult to find any interactive and visual content, thank you! I just finished my computer science bachelor and I find a great interest in these types of problems, could you recommend me an introductory book?
@VisuallyExplained
@VisuallyExplained 3 жыл бұрын
Awesome! Convex Optimization by Boyd and Vandenberghe is really good. The first author has his lectures on youtube as well if you're interested.
@hyperduality2838
@hyperduality2838 Жыл бұрын
@@VisuallyExplained From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law of thermodynamics all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Teleological physics (syntropy) is dual to non teleological physics (entropy). Duality creates reality. "Always two there are" -- Yoda. Points are dual to lines -- the principle of duality in geometry.
@benjaminbenjamin8834
@benjaminbenjamin8834 2 жыл бұрын
I appreciate this video but there was nothing related to primal and dual concepts in this video?
@rylanschaeffer3248
@rylanschaeffer3248 3 жыл бұрын
You have an extra negative at 7:59, I think.
@VisuallyExplained
@VisuallyExplained 3 жыл бұрын
Correct! I will compile a list of typos and add it to the description. Thank you!
@dempstert2712
@dempstert2712 2 жыл бұрын
At 3:12, did you mean to say hᵢ(x)≤ 0 and -hᵢ(x) ≥ 0 ? Such that the overlap of the two functions is linear?
@VisuallyExplained
@VisuallyExplained 2 жыл бұрын
"hᵢ(x)≤ 0" and "-hᵢ(x) ≥ 0" are actually the same thing.
@olivier306
@olivier306 Жыл бұрын
beautiful
@Tibug
@Tibug Жыл бұрын
These videos are marvelous(!) but you need a better mic.
@osamazaheer6430
@osamazaheer6430 2 жыл бұрын
great. Thanks
@wokeclub1844
@wokeclub1844 2 жыл бұрын
Great video!! Can Someone please explain How at 3:11 the equality Can be considered as those two inequalities?
@VisuallyExplained
@VisuallyExplained 2 жыл бұрын
sure, let's take an example. The equality x = 1 is equivalent to x >= 1 and x
@hyperduality2838
@hyperduality2838 Жыл бұрын
From a convergent, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law of thermodynamics all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. Homology (convergence, syntropy) is dual to co-homology (divergence, entropy). Teleological physics (syntropy) is dual to non teleological physics (entropy). Duality creates reality. "Always two there are" -- Yoda. Points are dual to lines -- the principle of duality in geometry.
@sygmermartins6082
@sygmermartins6082 2 жыл бұрын
very nice :)
@VisuallyExplained
@VisuallyExplained 2 жыл бұрын
Thank you! Cheers!
@aswathik4709
@aswathik4709 Жыл бұрын
6:51 is the lhs f(x)?
@blueberry23
@blueberry23 5 ай бұрын
@Throwingness
@Throwingness Жыл бұрын
Who named the friggin things 'primal' and 'dual'? It's confusing. 'Primal' is fine. 'Dual' makes it sound like we're dealing with two more of something. As we have three now.
@korayyy440
@korayyy440 2 жыл бұрын
>Potato shape >Makes an egg
@eneserdogan34
@eneserdogan34 2 жыл бұрын
This is some serious gourmath shit.
@himanshuverma298
@himanshuverma298 5 ай бұрын
Bhai please be accurate
@tsunningwah3471
@tsunningwah3471 Ай бұрын
zbian
@tsunningwah3471
@tsunningwah3471 Ай бұрын
jnnjjjjjj
@tsunningwah3471
@tsunningwah3471 8 ай бұрын
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