Timeline for Invertibility of neural network as operator on Wasserstein space
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 21, 2021 at 6:12 | answer | added | Christian Bueno | timeline score: 1 | |
| Jul 21, 2021 at 4:09 | comment | added | Christian Bueno | Perhaps this isn't your intention, but to have this line up for the usual single-hidden-layer neural networks, shouldn't we instead want $\sigma(x;w,b) = \sigma(w\cdot x + b)$ instead of what you described in your guess (which has one of the input neurons with a constant weight of -1)? | |
| Jun 19, 2021 at 11:31 | comment | added | Benoît Kloeckner | @JochenGlueck is right, and the issue is worse than he states. You work like $\mathcal{P}_2(\mathbb{R}^D)$ were a vector space when it really is a convex subset of a (small) affine subspace of the vector space of finite signed Radon measure. Problem is wasserstein metric does not extend to a norm on that space (it behaves badly on affine segment). | |
| Jun 19, 2021 at 11:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 19, 2021 at 12:02 | comment | added | Jochen Glueck | Maybe I misunderstand something - but how can $S$ be surjective into $L_{2,\nu}(\mathbb{R}^D)$ when, actually, $S\rho \ge 0$ for each $\rho \in P_2(\mathbb{R}^d)$? | |
| Feb 19, 2021 at 10:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 22, 2020 at 10:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 22, 2020 at 9:24 | answer | added | Steve | timeline score: 1 | |
| Sep 16, 2020 at 21:18 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Sep 16, 2020 at 21:09 | history | asked | Minkov | CC BY-SA 4.0 |