This is a great article and its super helpful, thanks to whoever wrote it!
laGrenouille 8 hours ago [-]
Great visualizations. Really enjoyed having a well-written example where mathematical proofs directly help with understanding a practical application.
I wonder what would happen with this analysis if a momentum term was added to the gradient descent. It seems that it would fix the specific failure modes in the examples, but I wonder if there's a corresponding mathematical way of categorizing what kinds of functions can(not) be quickly optimized with GD + momentum.
Scene_Cast2 3 hours ago [-]
There is one very clear example that I ran across due to the reasons outlined in the article. If you have a wavelet and you're trying to slide it around to make it fit, that will fail spectacularly. There are lots of problems that boil down to basically the above.
The neural net answer is being able to spawn a wavelet at any position, as opposed to tweaking the position of an existing one.
xuzhenpeng 10 hours ago [-]
The animation is very good, making the article easy to understand
Guestmodinfo 9 hours ago [-]
We studied it in our peparation for college entrance exams in India. Though the detail the article goes in is exhaustive. But I thought that this maybe common or almost common knowledge.
We used to call it sandwich theorem
I wonder what would happen with this analysis if a momentum term was added to the gradient descent. It seems that it would fix the specific failure modes in the examples, but I wonder if there's a corresponding mathematical way of categorizing what kinds of functions can(not) be quickly optimized with GD + momentum.
The neural net answer is being able to spawn a wavelet at any position, as opposed to tweaking the position of an existing one.
https://en.wikipedia.org/wiki/Ham_sandwich_theorem