Query on interactive plot about amr

[christopher-beckham]

Hi @jingcx

If you look at the first gif, you can see 3 red points embedded in a 3d latent space, let's call them h1, h2, and h3. What is happening is that at each frame of the video, a blue point is generated by sampling some h_i and h_j (where i,j can be either of the 3) and generating interpolations between them by sampling a random alpha from a uniform(0,1) and computing h_mix = alpha*h_i + (1-alpha)*h_j. The concept also applies to higher dimensional spaces if the h's were not in 3 dimensions -- you're just interpolating along a line whose endpoints are defined by h_i and h_j.

In the second gif, you are interpolating along 3 points at the same time, so that would be computing something like h_mix = alpha1*h1 + alpha2*h2 + alpha3*h3, where all those alphas sum to 1 (you can sample these alphas by using a Dirichlet distribution). In this case however, we are interpolating between triplets. This corresponds to interpolating within a triangle whose vertices are determined by h1,h2,h3. If we were doing 4 points instead, you'd be interpolating within a tetrahedron, etc. (Also see this for reference: https://en.wikipedia.org/wiki/Simplex)

The Bernoulli example is a bit less intuitive, it's not doing interpolation within line segments but something else which is more akin to extrapolation.

If it's still unclear, I would suggest you write a little example and use matplotlib (with 3d scatterplots) to visualise the types of interpolations you can do.

hth

[jingcx]

@christopher-beckham
Your explanation is very clear, and thank you so much for your patient!

[christopher-beckham]

Hi,

I generated the frames manually with matplotlib (a new interpolated point is added in each frame), and used ffmpeg to compile an mp4 out of the images.

[jingcx]

hello, I still confusing about the 3-D plots showed in the paper, which were represented as mixup/triplet mixup/Bernoulli mixup. Can you explain how to interpret these mixup methods as interpolating along line segments.
Thanks!

[christopher-beckham]

It's probably worth me putting up a Colab notebook of my own code that generated the figures. I will get to that shortly.