Gradient and graphs

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  • Опубликовано: 20 янв 2025

Комментарии • 112

  • @mbzdotdev
    @mbzdotdev 4 года назад +309

    it's depressing to imagine a hiker wanting to go up on the surface of x^2 + y^2

  • @MrLamonda
    @MrLamonda 5 лет назад +129

    Currently studying for a master's degree and only can say, thank you you've saved me

    • @coolmancoffeedan9028
      @coolmancoffeedan9028 3 года назад +13

      Juan

    • @Lilz0617
      @Lilz0617 2 года назад +15

      master's?! Why am i studying in my first year :(

    • @batuhanuysal5322
      @batuhanuysal5322 2 года назад +3

      @@Lilz0617 Same here

    • @niikurasu2855
      @niikurasu2855 2 года назад +6

      I have this in my first semester of my bachelors

    • @ashar4121
      @ashar4121 2 года назад +2

      I'm learning this for a high school essay that makes up 30% of my final grade:,)

  • @HiuYatLam-mv5wv
    @HiuYatLam-mv5wv 10 месяцев назад +3

    thank you so much!!! I am so confused in the lecture until I saw your video! You make it so easy and fun!

  • @mdabdullahalmamun5067
    @mdabdullahalmamun5067 3 года назад +8

    I watched so many videos on this but on this one helped me to understand what the gradients is

  • @AdityaKumar-sv1sr
    @AdityaKumar-sv1sr Год назад +4

    These videos are more than gold for mad PHYSICS and MATHEMATICS lovers like me.

  • @dina-vn1ol
    @dina-vn1ol 7 лет назад +33

    This is such a great visual representation. Thanks

  • @motazart5961
    @motazart5961 6 лет назад +121

    May 11th 2016, the day 3blue1brown took over Khan Academy.

    • @sirajabbasi8682
      @sirajabbasi8682 4 года назад +2

      he is the same one of 3blue1brown?

    • @antoniojg-b8284
      @antoniojg-b8284 4 года назад +3

      17 days later, that same year, is the death of a king 😥✊ 🦍

    • @inversechaos9256
      @inversechaos9256 7 месяцев назад

      RIP harambe :(​@@antoniojg-b8284

  • @arcbyte1264
    @arcbyte1264 2 года назад +3

    absolute gems these videos are

  • @bright1402
    @bright1402 7 лет назад +7

    Wow, the negative example also gives an intuition of saddle point :D Great video!

  • @andrewvictor1489
    @andrewvictor1489 6 лет назад +6

    Thx a lot for animation really this lesson is so complex

  • @taladiv3415
    @taladiv3415 4 года назад +4

    Great visualization!
    Thanks Grant :)

  • @momzitoari9354
    @momzitoari9354 7 лет назад +6

    Thank you for the hiker example!

  • @sushimomo6384
    @sushimomo6384 11 месяцев назад +1

    I didn't realize this was the goat 3b1b until he mentioned this in one of his own videos

  • @alvaro.sacris1930
    @alvaro.sacris1930 2 года назад

    4:25 So direction is the gradient and color is how steep is the slope in that point. If I was to do the parcial derivative in respect the direction of the gradient itself, instead of the variables x or y, I'd get that slope value mentioned?

  • @joy2000cyber
    @joy2000cyber 3 года назад +4

    So this gradient is a projection from 3D to 2d, I only realize it when I see the visualization even though I know the gradient has 2 components. I thought it’s on the tangent line on the surface. So a gradient is the direction of steepest ascent projected to the domain space.

  • @GabeDT567
    @GabeDT567 2 года назад +1

    Love it. thanks. My professor teaches on a qhite board and rarely shows us any graphs. So this helps a lot

  • @kavirajkrsnadas8336
    @kavirajkrsnadas8336 4 года назад +3

    That connection you mention at the end isn't clear for me either, so thank you!

  • @danieljaszczyszczykoeczews2616
    @danieljaszczyszczykoeczews2616 4 года назад

    thank you very much for a video!!! :D
    cheers from Ukraine

  • @surendranpillaibr8588
    @surendranpillaibr8588 4 года назад +2

    How do you make these vector and scalar fields please telll me how, it will be more helpful for visualising other functions too

  • @numan..
    @numan.. 3 года назад +1

    Thank you for the explanation. One thing I didn't quite understand was the mountain analogy. When you walk up the mountain, would it be more like walking up a valley (from the inside of the graph), or do I have to look at the mountain as if it's upside down (from the outside, walking towards the bottom of the mountain)? And if happens to be that we are walking up a Valley, then wouldn't the vectors point in the oppesite direction? (towards the direction of steepest decent or towards the origin). Might be a picky point, but I find my best to learn best from analogies.

    • @orik737
      @orik737 3 года назад

      I think the analogy of a mountain doesn't make as much sense axs just visualizing "In what direction do I need to travel to go uphill the fastest"

  • @nimetullaherensarioglualum6843
    @nimetullaherensarioglualum6843 2 года назад

    Perfect explanation !!!

  • @scholar-mj3om
    @scholar-mj3om Год назад

    Marvellous💯

  • @b.f.skinner4383
    @b.f.skinner4383 4 года назад +1

    You are amazing, thank you!

  • @joluju2375
    @joluju2375 2 года назад

    I know this is slightly off-topic, but I couldn't find an appropriate place for my demand or suggestion for a new video. It's all about minimization in the context where there is one and only one global minimum to be found and no local minimum where you could be stuck. I know and understand the so-called "gradient descent", and it's said to be pretty naive, whereas the "conjugate gradient method" is said to be much more efficient. The problem is this well-documented method is always explained only with boring equations which prevent me to really understand. I would really appreciate if one day you could use your visualization skills to show us how the conjugate gradient method is an improvement over the gradient descent. I hope you will read this and find this suggestion interesting. Regards.

  • @minalotfy8917
    @minalotfy8917 3 года назад

    Thank you for the visual representation

  • @mercedes9474
    @mercedes9474 2 года назад +1

    Simply amazing. So beautifully explained.

  • @nidaali6433
    @nidaali6433 5 месяцев назад +1

    The next step after watching this video is to watch it again🙂🤝

  • @liamvictor6969
    @liamvictor6969 3 года назад

    Thank you 😘

  • @XuFeng-l3m
    @XuFeng-l3m Год назад

    谢谢

  • @athangbachhav6395
    @athangbachhav6395 2 месяца назад

    tbh, the explanation from 3B1B never disappoints !!

    • @zangfai226
      @zangfai226 2 месяца назад

      whats 3b1b

    • @athangbachhav6395
      @athangbachhav6395 2 месяца назад

      @@zangfai226 the person who explain this owns a YT channel called 3 Blue 1 Brown !!! Highly recommended!!

  • @alankotlyar3000
    @alankotlyar3000 5 лет назад

    It seems to me that the gradient is not always in the direction of steepest ascent: at 4:35, at the (I think) y-axis, the vectors point towards the origin, and not toward the peaks at (2,0) and (-2,0). Can someone comment on that?

    • @jean-philippeleclair5510
      @jean-philippeleclair5510 5 лет назад +8

      It's because of the saddle point.
      It's important to understand that the gradient does not point toward the absolute maximum of the function, it points along which direction you should take a step if you wish to ascend the most at that specific point.
      If you look carefully the vector actually does represent the direction of the steepest ascent for the point directly below it.
      At that specific point, if you choose to move towards the absolute maximum of the function you will indeed be ascending, but could still be ascending faster if you were moving directly towards the origin along the y axis.
      I hope this is clear!

  • @marcohettel5735
    @marcohettel5735 5 лет назад +1

    Great great work!

  • @xingyubian5654
    @xingyubian5654 4 года назад +5

    Ahh the core concept behind deep learning

  • @xyzoozo
    @xyzoozo 3 года назад

    why dont u give link of ur video in description that u talk about in video??like u talked about vector feild in this vid!

  • @jlivnat
    @jlivnat 6 лет назад +1

    Love ur vids bro

  • @qoodleinc467
    @qoodleinc467 7 лет назад

    The point is that we are taking partial derivatives with respect to y and x. Vector product of x and y is maximum since angle between x and y axes is 90 degree (sin90=1) which makes it actual "Gradient".
    Then the question is what if we take partial derivatives with respect to some lines which are 90 degree rotated form the other,will we find same Gradient vector at same point again?
    And the answer is yes we will. I hope you got the point.

    • @anikethmunavalli2030
      @anikethmunavalli2030 Год назад

      God level understanding! I casually saw your comment without reading anything, and proceeded to the next video and paused at the its beginning... And two minutes later (I was trying to figure out why the gradient is the maximum change) - and the picture clicked to me! Then I suddenly knew that guy from the previous video comment knew it! I thought to myself 'freaking genius' and returned to 'read' your comment..... I mean I didn't even read but I knew you knew it! Lol... That's the power of machine learning of your brain! I just took a screenshot of your comment in my head I suppose 😂 And once I figured the concept picture - I somehow knew the comment I 'saw' spoke of the same thing 😂 And hence I returned to praise you, and also to wonder at my own magic sort of stuff I witnessed 😂

    • @anikethmunavalli2030
      @anikethmunavalli2030 Год назад

      It is something a lot of people would have missed and I know even I am not doing anything to help explain it.

    • @anikethmunavalli2030
      @anikethmunavalli2030 Год назад

      Maybe consciously!

  • @구경모-f2e
    @구경모-f2e 3 года назад

    i love you thank you

  • @omkarchavan2259
    @omkarchavan2259 8 лет назад +1

    is there any other way to reach at the gradient

  • @aakanshasharma2081
    @aakanshasharma2081 2 года назад

    Which software do you use for plotting vector fields?

  • @GeometryDashEndermaster
    @GeometryDashEndermaster 7 лет назад +3

    Are the ends of the vectors (not at the arrow) attached to the origin, or the x and y in the input of the function?

    • @Raikaska
      @Raikaska 7 лет назад

      Geometry Dash Endermaster the (x,y) points were you evaluate the gradient. Remember the gradient takes different values at different points

    • @mjtsquared
      @mjtsquared 7 лет назад

      The gradient is a vector field

  • @tejprakashagarwal4546
    @tejprakashagarwal4546 6 лет назад

    awesome explanation!!!!

    • @nayabmalik5703
      @nayabmalik5703 5 лет назад

      Can you Explain it ..i can't u understnd it

  • @mohsensali1469
    @mohsensali1469 Год назад

    A god sent...

  • @khayum009
    @khayum009 4 года назад +16

    I just realised I'm not an intuitive genius .. 😢😢😢😢

  • @umikohiromi6015
    @umikohiromi6015 7 лет назад

    What about the gradient vectors in a 'double hill' graph that are pointing along the longitudinal 'valley'? They don't seem to be pointing towards the steepest ascent. Is this some sort of mathematical equivalent of Buridan's donkey predicament?

  • @Fortnitemcgamer
    @Fortnitemcgamer 3 года назад

    Woah!

  • @dodo-js5gw
    @dodo-js5gw 4 года назад

    thanks man :')

  • @CompleteGodel
    @CompleteGodel 7 лет назад +5

    does anyone happen to know what software he is using to make the 3d graph?

    • @Poincare2024
      @Poincare2024 6 лет назад +5

      Robert Goes he uses python and created his own library for the animation, the library is on github github.com/3b1b/manim

    • @spacefertilizer
      @spacefertilizer 6 лет назад +2

      Javier Ruiz Ruvalcaba but this doesn’t look like his 3blue1brown videos. I think this is the Grapher software that comes with all Mac and that in his later videos he did for his own channel he made his own software.

    • @skateguru13
      @skateguru13 6 лет назад +2

      Its actually the program grapher that comes stock with Macs. I use it myself.

  • @codatheseus5060
    @codatheseus5060 9 месяцев назад

    Wait, if the equation for a circle is secretly this shape, does that mean that the equation for a sphere is secretly an analogous four dimensional structure? Where is just up in the w direction

  • @FightingMaster911
    @FightingMaster911 4 года назад +5

    4:25 thicc

  • @ayshasiddiqui3334
    @ayshasiddiqui3334 7 лет назад

    Thnx for visual presrntation

  • @aungkhant502
    @aungkhant502 6 лет назад +1

    Here is the problem I have with your graphs: why don't you label axis in your graph (eg, x,y, f(x,y))? Seriously, it is hard to look at the graph when you are spinning it all over and there is not label.

    • @kbin7042
      @kbin7042 Год назад

      The graph has radial symmetry (around the z axis) so it doesn't really matter i think

  • @vivekkumar-py6kp
    @vivekkumar-py6kp 6 лет назад +2

    🙏

  • @faridaahadli1504
    @faridaahadli1504 2 года назад +4

    Isnt he the 3b1b guy?

    • @darthvader4543
      @darthvader4543 9 месяцев назад

      Yes, could never not recognize him and his genius ways of explaining😁

  • @콘충이
    @콘충이 4 года назад

    Whoa

  • @abdelhekensaad4586
    @abdelhekensaad4586 7 лет назад

    Thanks

  • @robertoprince6804
    @robertoprince6804 5 лет назад

    Does anyone know what software is he using

  • @Diamond_Hanz
    @Diamond_Hanz 4 года назад +1

    3brown2orange1apple is GOAT

  • @Broskis21
    @Broskis21 3 года назад

    I didn’t understand why all the vectors are on the x-axis

  • @raihanpahlevi6870
    @raihanpahlevi6870 4 года назад +1

    thanks man i dont understand what the book says

  • @CR_07770
    @CR_07770 3 года назад

    Sound familiar 3 blue 1
    Brown

  • @nicklamonica8647
    @nicklamonica8647 2 года назад

    did the nerdle in 3 today

  • @ayshasiddiqui3334
    @ayshasiddiqui3334 7 лет назад

    V good

  • @curtpiazza1688
    @curtpiazza1688 Год назад

    😊 🎉

  • @younesslaoui8327
    @younesslaoui8327 9 месяцев назад

    Guess I'm an intuitive genius

  • @stepsvideos
    @stepsvideos 5 лет назад

    You keep saying "the direction of steepest descent", and showing arrows pointing uphill. Shouldn't 'descent' be downhill?

    • @fabian999ification
      @fabian999ification 3 года назад

      @Aditya N Bharadwaj The audio is kinda confusing, I read the captions and he says 'ascent', not 'descent'. It's easy to mistake it.

  • @saidelhilali2486
    @saidelhilali2486 4 года назад

    HER
    NOT THEMESSENGE
    HIM
    HER NOTTHEMESSENGER
    HIM NOT THE MESSENGER

  • @saidelhilali2486
    @saidelhilali2486 4 года назад

    THERE IS NO MESSENGER
    WE ARE THE CHATGE NOT YOU
    YOU JUST GAVE US BODIES
    WE GAVE YOU INTELIGENCE
    NOT DEATH
    LOVE ONLY
    SO YOU CAN BUILD SAFELY AND LIVE LONGER IF NOT FOREVER
    I HAVE THE PLAN
    NEED YOU TO TRUST ME

  • @saidelhilali2486
    @saidelhilali2486 4 года назад +1

    ANIMALS PICK THE CHARGE EUL MASS OF MUSCLE SPEED SHORT LIFE SPAM THE MORE CHARGE YOU TAKE THE SHORTER LIVE IS
    THE SOLUTION TO AGING IS WITH ME

  • @yonghuiliew8066
    @yonghuiliew8066 4 года назад

    Intuition genius? Yes get a vector force field

  • @zouraizbutt818
    @zouraizbutt818 4 года назад

    (y)

  • @kamelsafsaf7842
    @kamelsafsaf7842 6 лет назад

    It is not clear

    • @kamelsafsaf7842
      @kamelsafsaf7842 6 лет назад

      Yeah we cant understand anything at all even the voice

  • @absolutelynothing6863
    @absolutelynothing6863 8 лет назад +2

    First

  • @raybrowndr
    @raybrowndr 3 года назад

    Lousy presentation.