3 ms·

Interpreting neural networks through the polytope lens (2022)

80 points by sva_ 3y ago

samstave 3y ago
I wonder if these two things from the HN post below this one: https://www.nature.com/articles/d41586-024-00288-1 https://www.nature.com/articles/d41586-024-00288-1 I would love to see a cross section of these two ideas.... I have been surprised that in the past few weeks, I have seen several posts on HN where, while separate, unrelated posts here - there have been related characteristics and if you look at them for a sec, you can see how having AIs GPT both studies/papers - immediate connections worth looking at further are revealed. If even for the sake of just a more informed tapestry of knowledge in a particular area... Its really enjoyable reading and TIL'ing.
- data_maan 3y ago
  These ideas are too far apart...
adamnemecek 3y ago
I’m very much exploring this idea. Hopf algebras provide a really nice wrapper around this. I have a discord to discuss this https://discord.cofunctional.ai https://discord.cofunctional.ai
Scene_Cast2 3y ago
I wonder if there's a way to learn polytopes directly with a non-MLP formulation.
- jtanderson 3y ago
  There are many interesting efforts — going back quite a few years —- to this goal, many of which in the PAC setting (which automatically means MLP is out, for theoretical guarantees). E.g [0]and its related references come to mind as an interesting place to look into it! [0]: https://proceedings.neurips.cc/paper/2018/file/22b1f2e0983160db6f7bb9f62f4dbb39-Paper.pdf https://proceedings.neurips.cc/paper/2018/file/22b1f2e098316... pro (Edited for some clarity)
anon291 3y ago
Very interesting read and a rather "obvious" one. I can't believe I didn't see this before. Obviously... A perceptron layer is a bunch of dot products followed by comparison. Every graphics programmer knows this is a check of which side of a plane you're on. Of course, the relu unit is also a passing on information when the result is on one side of the plane, making this a spline. As others have said... Can we learn the separating planes without the backward gradient propagation? I don't know but seeing it in this new way may help.
Nevermark 3y ago
> if we scale the activations in a particular layer in a non-linear network, some neurons in later layers may ‘activate’ or ‘deactivate’. Normalization removes this problem. Magnitude information can still be encoded separately in a log form so differentiation can still happen when scale matters, but scaling doesn't have much impact by default (small initial weights following magnitude element).

80 points by sva_ 3y ago

I wonder if these two things from the HN post below this one: https://www.nature.com/articles/d41586-024-00288-1 https://www.nature.com/articles/d41586-024-00288-1 I would love to see a cross section of these two ideas.... I have been surprised that in the past few weeks, I have seen several posts on HN where, while separate, unrelated posts here - there have been related characteristics and if you look at them for a sec, you can see how having AIs GPT both studies/papers - immediate connections worth looking at further are revealed. If even for the sake of just a more informed tapestry of knowledge in a particular area... Its really enjoyable reading and TIL'ing.

data_maan 3y ago
These ideas are too far apart...

adamnemecek 3y ago

I’m very much exploring this idea. Hopf algebras provide a really nice wrapper around this. I have a discord to discuss this https://discord.cofunctional.ai https://discord.cofunctional.ai

Scene_Cast2 3y ago

I wonder if there's a way to learn polytopes directly with a non-MLP formulation.

jtanderson 3y ago
There are many interesting efforts — going back quite a few years —- to this goal, many of which in the PAC setting (which automatically means MLP is out, for theoretical guarantees). E.g [0]and its related references come to mind as an interesting place to look into it! [0]: https://proceedings.neurips.cc/paper/2018/file/22b1f2e0983160db6f7bb9f62f4dbb39-Paper.pdf https://proceedings.neurips.cc/paper/2018/file/22b1f2e098316... pro (Edited for some clarity)

anon291 3y ago

Very interesting read and a rather "obvious" one. I can't believe I didn't see this before. Obviously... A perceptron layer is a bunch of dot products followed by comparison. Every graphics programmer knows this is a check of which side of a plane you're on. Of course, the relu unit is also a passing on information when the result is on one side of the plane, making this a spline. As others have said... Can we learn the separating planes without the backward gradient propagation? I don't know but seeing it in this new way may help.

Nevermark 3y ago

> if we scale the activations in a particular layer in a non-linear network, some neurons in later layers may ‘activate’ or ‘deactivate’. Normalization removes this problem. Magnitude information can still be encoded separately in a log form so differentiation can still happen when scale matters, but scaling doesn't have much impact by default (small initial weights following magnitude element).