Should gradient descent create a path that is always perpendicular to contour lines?

[rmwkwok]

Hello @neirar,

It has been some time, but in case it helps, you may check this post out for a GIF that shows the magic. So, for your first question, I think it is not a bug.

C1W1 Lab04, why aren't the gradients perpendicular to the contour lines?

Hello Eric, I believe that is because our impression of the “right angle” is always based on that we have an 1:1 image aspect ratio. Check this out: [Project001 (3)] [contour] The GIF shows how changing the aspect ratio “correct” our “right angle”. The code controlled the aspect ratio with the figure size and the ranges of w and b, so you may change those settings to make it 1:1 like what I have done below: [image] As you can see (1) same range for both w and b, and (2) a square image. …

Btw, what do you think now about the second question? I guess the first thing would be: how do you define a plane, for example, in our 2-parameter example?

Cheers,
Raymond