Gradient and graphs
Вставка
- Опубліковано 10 тра 2016
- Learn how the gradient can be thought of as pointing in the "direction of steepest ascent". This is a rather important interpretation for the gradient.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy: ua-cam.com/users/subscription_...
it's depressing to imagine a hiker wanting to go up on the surface of x^2 + y^2
true
A skateboarder would love to go down on it.
more like - x² - y²
Currently studying for a master's degree and only can say, thank you you've saved me
Juan
master's?! Why am i studying in my first year :(
@@Lilz0617 Same here
I have this in my first semester of my bachelors
I'm learning this for a high school essay that makes up 30% of my final grade:,)
thank you so much!!! I am so confused in the lecture until I saw your video! You make it so easy and fun!
May 11th 2016, the day 3blue1brown took over Khan Academy.
he is the same one of 3blue1brown?
17 days later, that same year, is the death of a king 😥✊ 🦍
RIP harambe :(@@antoniojg-b8284
These videos are more than gold for mad PHYSICS and MATHEMATICS lovers like me.
This is such a great visual representation. Thanks
I watched so many videos on this but on this one helped me to understand what the gradients is
Great visualization!
Thanks Grant :)
Thank you for the hiker example!
absolute gems these videos are
Simply amazing. So beautifully explained.
Love it. thanks. My professor teaches on a qhite board and rarely shows us any graphs. So this helps a lot
You are amazing, thank you!
Thx a lot for animation really this lesson is so complex
Wow, the negative example also gives an intuition of saddle point :D Great video!
Thank you for the visual representation
Great great work!
That connection you mention at the end isn't clear for me either, so thank you!
Ahh the core concept behind deep learning
Love ur vids bro
Perfect explanation !!!
Thanks!
thank you very much for a video!!! :D
cheers from Ukraine
I didn't realize this was the goat 3b1b until he mentioned this in one of his own videos
Marvellous💯
谢谢
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.
Woah!
Thank you 😘
I just realised I'm not an intuitive genius .. 😢😢😢😢
thanks man :')
Thnx for visual presrntation
How do you make these vector and scalar fields please telll me how, it will be more helpful for visualising other functions too
A god sent...
It seems intuitive to me that the gradient is the fastest. Each partial derivative is the slope of the fastest line that still hugs the curve locally and they effect eachother's influence on the trajectory
I don't understand what you are talking about. But from watching the videos about directional derivatives, and how it's a dot product of the vector and the gradient, the directional derivative is maximized when the vector is in the same direction, since dot products are maximized with vectors with 0 angle. Thus the vector chosen should be the gradient itself, to maximize the dot product, or in other words the directional derivative. Thus, maximizing the directional derivative is finding the direction of steepest ascent, which is the gradient itself.
i love you thank you
Which software do you use for plotting vector fields?
Thanks
awesome explanation!!!!
Can you Explain it ..i can't u understnd it
Whoa
is there any other way to reach at the gradient
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.
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"
🙏
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.
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!
4:25 thicc
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.
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 😂
It is something a lot of people would have missed and I know even I am not doing anything to help explain it.
Maybe consciously!
V good
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?
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?
Geometry Dash Endermaster the (x,y) points were you evaluate the gradient. Remember the gradient takes different values at different points
The gradient is a vector field
3brown2orange1apple is GOAT
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?
does anyone happen to know what software he is using to make the 3d graph?
Robert Goes he uses python and created his own library for the animation, the library is on github github.com/3b1b/manim
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.
Its actually the program grapher that comes stock with Macs. I use it myself.
😊 🎉
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
Isnt he the 3b1b guy?
Yes, could never not recognize him and his genius ways of explaining😁
did the nerdle in 3 today
Does anyone know what software is he using
It’s Manim
thanks man i dont understand what the book says
Sound familiar 3 blue 1
Brown
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?
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!
I didn’t understand why all the vectors are on the x-axis
Guess I'm an intuitive genius
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.
The graph has radial symmetry (around the z axis) so it doesn't really matter i think
(y)
You keep saying "the direction of steepest descent", and showing arrows pointing uphill. Shouldn't 'descent' be downhill?
@Aditya N Bharadwaj The audio is kinda confusing, I read the captions and he says 'ascent', not 'descent'. It's easy to mistake it.
HER
NOT THEMESSENGE
HIM
HER NOTTHEMESSENGER
HIM NOT THE MESSENGER
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
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
First
and only
What is first
Intuition genius? Yes get a vector force field
It is not clear
Yeah we cant understand anything at all even the voice