Adrian Xu’s MSc thesis contains an idea called “radial trace plots” which could be explored further. We care a lot about local geometry but in high dimensions it’s not clear that there are meaningful ways to visualize it (the pictures one usually sees of loss landscapes are imo dumb / highly misleading). I think this isn’t what you had in mind by “n dimensional data visualizations” but people are very visual, and communicating degeneracy by some actually meaningful visualizations might be something to look into if you’re interested in learning SLT. Daniel Murfet suggested this when I asked him for shovel ready devinterp projects, but I ended up not working on it.
Could you send a link to the “radial trace plots” work? I can’t seem to find anything.
I mostly agree with you about the loss landscape issue. It’s only looking at loss as a fn of a 2d subspace which is extremely limiting if you’re trying to make sense of a space with thousands or millions of dimensions.
in high dimensions it’s not clear that there are meaningful ways to visualize it
I think the question of whether or not it is possible to meaningfully visualize it is of prime importance to my work. My intuition is of course that it is possible. Very generally, my goal is to develop a “visual language” which serves as a memory aid, and set of tools for controlling “viewport rotation”, then in the same way that a 3d object can be understood as 3d by rotating it in your hands, a m<n dimensional subspace with properties of interest can be found in a region of a distribution, and the md distribution can be understood as md by rotating it and recalling it’s rotation dynamics with the help of interaction and visual hints.
But this seems like a difficult thing to communicate just with words. As I mention in this post, it is inspired by the work of Mingwei Li, particularly Grand Tour and UMAP Tour. If you haven’t glanced at those that might give you a much better intuition of the direction I’m thinking, but I have many additional ideas I need to document at some point, especially relating to a “visual language”.
I had not previously heard about SLT, but it looks like it is very relevant to my interests, so thank you very much for mentioning it. I will definitely work it into my study plans somewhere.
Adrian Xu’s MSc thesis contains an idea called “radial trace plots” which could be explored further. We care a lot about local geometry but in high dimensions it’s not clear that there are meaningful ways to visualize it (the pictures one usually sees of loss landscapes are imo dumb / highly misleading). I think this isn’t what you had in mind by “n dimensional data visualizations” but people are very visual, and communicating degeneracy by some actually meaningful visualizations might be something to look into if you’re interested in learning SLT. Daniel Murfet suggested this when I asked him for shovel ready devinterp projects, but I ended up not working on it.
Could you send a link to the “radial trace plots” work? I can’t seem to find anything.
I mostly agree with you about the loss landscape issue. It’s only looking at loss as a fn of a 2d subspace which is extremely limiting if you’re trying to make sense of a space with thousands or millions of dimensions.
I think the question of whether or not it is possible to meaningfully visualize it is of prime importance to my work. My intuition is of course that it is possible. Very generally, my goal is to develop a “visual language” which serves as a memory aid, and set of tools for controlling “viewport rotation”, then in the same way that a 3d object can be understood as 3d by rotating it in your hands, a m<n dimensional subspace with properties of interest can be found in a region of a distribution, and the md distribution can be understood as md by rotating it and recalling it’s rotation dynamics with the help of interaction and visual hints.
But this seems like a difficult thing to communicate just with words. As I mention in this post, it is inspired by the work of Mingwei Li, particularly Grand Tour and UMAP Tour. If you haven’t glanced at those that might give you a much better intuition of the direction I’m thinking, but I have many additional ideas I need to document at some point, especially relating to a “visual language”.
I had not previously heard about SLT, but it looks like it is very relevant to my interests, so thank you very much for mentioning it. I will definitely work it into my study plans somewhere.
Sure, I sent you the file over discord.