Answers.Body: <p>It represents the value of the loss function <code>J(x1, x2; θ)</code>; the valley has value 0 in the video. You can see that the lowest ball with value 3.13 is on a steep point with a high gradient, so it's not the gradient. </p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-04-11T10:57:26.643Z
Answers.LastActivityDate: 2020-04-11T10:57:26.643Z
Answers.UserDisplayName: olix20
Body: <p>The following image is a screenshot from <a href="https://youtu.be/_7JKYazD0ew" rel="nofollow noreferrer">a video tutorial</a> that illustrates the concept of gradient descent algorithm with a 3D animation.</p>
  
  <p>Do the numbers on the top of the balls pointed out by the red arrows represent the gradient?</p>
  
  <p><a href="https://i.sstatic.net/QG3Cy.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/QG3Cy.jpg" alt="enter image description here"></a></p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-04-10T22:48:00.793Z
Comments.Text: When you say "Are the numbers on the top of the balls are their gradient descent?", do you mean "gradient" (and not "gradient descent"), right? I think so, thus I edited your post to reflect this. Also, note that you were watching a video that has already 2 dislikes, so that may be a good sign that you shouldn't even watch that video.
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-04-11T00:16:18.107Z
Comments.Text: @nbro With your reminder I realize that, thank you. Could you explain a bit more about the mistake in that video? For example, gradient usually ranges between (-1.0, 1.0), is my understanding right?
Comments.UserDisplayName: Piete3r
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-04-11T00:18:57.060Z
Comments.Text: I am not saying that the video is showing the wrong info. The gradient is a vector and the values of the elements of this gradient (i.e. a vector) aren't really restricted to a range. The values depend on the loss function. I think you should investigate a little bit more about derivatives, gradients, etc., then ask a more specific question.
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-04-11T00:41:45.980Z
Comments.Text: @nbro Thank you. My OP is asking a specific question and your comment to that question is appreciated. I guess I understand the basic idea about derivatives, gradients in general.  The range of (-1.0, 1.0) I use is specifically for the discussion in the context of deep learning, where all features are typically normalized. Please correct my misunderstanding. Sorry for misleading.
Comments.UserDisplayName: Piete3r
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-04-11T00:42:57.803Z
Comments.Text: Well, yes, typically, you don't want the gradient to take very big or very small numbers, but this not guaranteed, and, as you say, it may also depend on the activation functions that you use. Have a look at the exploding and vanishing gradient problems.
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-04-11T00:47:48.467Z
Comments.Text: @nbro I also appreciate your reminder for that video.I'd just like to know whether the video conveys something that might be misleading. If yes, which part it is. Neither like nor dislike helps my understanding of the particular concept in my OP, that is, the concept of gradient descent.
Comments.UserDisplayName: Piete3r
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-04-11T01:25:26.753Z
Comments.Text: That video isn't very useful that's why it was disliked. I encourage you to look for other sources about GD. The gradient is a vector, but that animation doesn't show those points as vectors. Those points could represent the loss at specific values or they could represent the parameters of the loss function that minimize the loss function.
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-04-11T02:11:56.533Z
Comments.Text: @nbro Got it. You gave me so much helpful information and leads. Thank you so much. Would you mind copy them to answer? I'll accept it.
Comments.UserDisplayName: Piete3r
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-04-11T02:15:55.913Z
Comments.Text: Ok, I will do that (maybe a little later)!
Comments.UserDisplayName: nbro
Tags: <terminology><objective-functions><gradient-descent>
Title: What do these numbers represent in this picture of a surface?
UserDisplayName: Piete3r
ThreadText: # What do these numbers represent in this picture of a surface?
  
  (Asked by: username_0 on 2020-04-10)
  
  The following image is a screenshot from [a video tutorial](https://youtu.be/_7JKYazD0ew) that illustrates the concept of gradient descent algorithm with a 3D animation.
  
  Do the numbers on the top of the balls pointed out by the red arrows represent the gradient?
  
  [![enter image description here](https://i.sstatic.net/QG3Cy.jpg)](https://i.sstatic.net/QG3Cy.jpg)
  
  **Tags:** terminology, objective-functions, gradient-descent
  > **Comments:**
  > **username_1**: When you say "Are the numbers on the top of the balls are their gradient descent?", do you mean "gradient" (and not "gradient descent"), right? I think so, thus I edited your post to reflect this. Also, note that you were watching a video that has already 2 dislikes, so that may be a good sign that you shouldn't even watch that video.  
  > **username_0**: @nbro With your reminder I realize that, thank you. Could you explain a bit more about the mistake in that video? For example, gradient usually ranges between (-1.0, 1.0), is my understanding right?  
  > **username_1**: I am not saying that the video is showing the wrong info. The gradient is a vector and the values of the elements of this gradient (i.e. a vector) aren't really restricted to a range. The values depend on the loss function. I think you should investigate a little bit more about derivatives, gradients, etc., then ask a more specific question.  
  > **username_0**: @nbro Thank you. My OP is asking a specific question and your comment to that question is appreciated. I guess I understand the basic idea about derivatives, gradients in general.  The range of (-1.0, 1.0) I use is specifically for the discussion in the context of deep learning, where all features are typically normalized. Please correct my misunderstanding. Sorry for misleading.  
  > **username_1**: Well, yes, typically, you don't want the gradient to take very big or very small numbers, but this not guaranteed, and, as you say, it may also depend on the activation functions that you use. Have a look at the exploding and vanishing gradient problems.  
  > **username_0**: @nbro I also appreciate your reminder for that video.I'd just like to know whether the video conveys something that might be misleading. If yes, which part it is. Neither like nor dislike helps my understanding of the particular concept in my OP, that is, the concept of gradient descent.  
  > **username_1**: That video isn't very useful that's why it was disliked. I encourage you to look for other sources about GD. The gradient is a vector, but that animation doesn't show those points as vectors. Those points could represent the loss at specific values or they could represent the parameters of the loss function that minimize the loss function.  
  > **username_0**: @nbro Got it. You gave me so much helpful information and leads. Thank you so much. Would you mind copy them to answer? I'll accept it.  
  > **username_1**: Ok, I will do that (maybe a little later)!  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2020-04-11. Score: 1
  
  It represents the value of the loss function `J(x1, x2; θ)`; the valley has value 0 in the video. You can see that the lowest ball with value 3.13 is on a steep point with a high gradient, so it's not the gradient.
  
  
  ---
  
  