Content deleted Content added
→Out of date: reply |
No edit summary |
||
Line 48:
::::: Thank you for your reply. (i) The fact that your conference paper is now published does not change the fact that it is your own work and so you are biased w.r.t. its importance. Also, being peer-reviewed is only a necessary, but not a sufficient condition to be included. There are several versions of this theorem, so which ones should we present? The general approach of WP is that we present the versions covered by secondary sources (scientific books, university textbooks, survey papers, etc.), even if it means that there is a delay in presenting the latest results. Remember that WP is for a general audience and not only for dedicated researchers of a specific field. (ii) I find Cybenko's proof instructive, but you are welcome to add Pinkus' version, if you think that it is simpler. If it is indeed better for WP readers, then we could remove Cybenko's proof. (iii) The statements of the presented theorems only contain the word "exist" without providing a specific formula for the weights, hence, at least the current formulations of the results are not constructive. Regarding the proofs, some of them are based on variants of the Stone–Weierstrass theorem, which means that they are not constructive. I do not know the proof technique that you used for your theorem, but if it provides an explicit construction for the network (given a target function <math>f</math>), then it would be good to highlight it. Cheers, [[User:Koertefa|''<span style="color:#2F4F4F">'''K'''<span style="color:Teal">œrte</span>'''F'''</span><span style="color:Teal">a</span>'']] [[User talk:Koertefa#top|<span style="color:#2F4F4F">'''{'''<i style="color:Teal">ταλκ</i>'''}'''</span>]] 12:45, 1 July 2020 (UTC)
:::::: @[[User:Koertefa|''<span style="color:#2F4F4F">'''K'''<span style="color:Teal">œrte</span>'''F'''</span><span style="color:Teal">a</span>'']] Thanks your response. Ordered from least thorny to most thorny:
::::::* Several versions of the theorem indeed do not rely on Stone--Weierstrass. (And off the top of my head, certain versions of Stone--Weierstrass actually are constructive, but I'm not sure about how in how general a setting constructivity is known - a Google search suggests that this is known in quite general settings, but perhaps you know more than I do on this topic?)
::::::* I think the most important point is the removal of Cybenko and the highlighting of Pinkus. (Which I feel unnecessarily complicates the article.) I'll try and write up a brief sketchproof for Pinkus.
::::::* Yeah, I realise one's own work is a thorny topic. You can see from the discussion above that I wasn't sure if I was okay discussing it, but was told that I should give it a go. I did talk to Themumblingprophet to review and avoid potential COI but they didn't get back to me.
::::::* If we use only secondary sources then unfortunately I think the whole "dual" formulation has to be removed. So be it; I'll do that when I remove Cybenko + add a sketchproof for Pinkus. Best, [[User:PatrickKidger|PatrickKidger]] ([[User talk:PatrickKidger|talk]]) 17:47, 1 July 2020 (UTC)
| |||