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== Deep variants ==
The two deep variants appear to be somewhat dubious. The citation is just a conference preceding, and it omits the proofs. If an expert knows any more reliable sources that would be ideal <!-- Template:Unsigned --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Pabnau|Pabnau]] ([[User talk:Pabnau#top|talk]] • [[Special:Contributions/Pabnau|contribs]]) 01:47, 21 April 2019 (UTC)</small> <!--Autosigned by SineBot-->
''Note on above comment: There is no issue with proceedings and they are peer-reviewed and carry heavyweight in the field, at times more than journals.''
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Hanin and Sellke's work are an improvement over Lu et al's because their result applies to general continuous functions, not just convex ones;
''The deep section of the page is a mess. I have cleaned up the shallow section to make it more legible but maybe someone can pickup the slack on the second part... it really is badly written.''
== Vague wording ==
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:::: For the above reasons I would like to revert your edits, but I'd prefer to have a discussion about it here first. [[User:PatrickKidger|PatrickKidger]] ([[User talk:PatrickKidger|talk]]) 08:51, 1 July 2020 (UTC)
::::: 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)
:::::::Thanks again for your reply. (i) Regarding constructivity: you are right that whether the proofs are [[Constructive proof|constructive]] is debatable (there are many versions of the theorem based on various proof techniques), and it might not even be important for an average reader. On the other hand, what I think is important is that it is an [[existence theorem]] that is, the theorem itself does not provide a construction for the object it claims to exist (irespectively whether the proofs are constructive in the sense of formal logic). So, the statements of the theorems do not provide methods / algorithms to build networks with the claimed approximation properties (though the proofs might have constructions). In my opinion, it is a crucial point. (ii) Regarding Pinkus' theorem: I agree with you that if it has a concise and instructive proof and we can present it, then we do not really need Cybenko's proof. We might even remove the classical version of the theorem (though, its advantage is that it is the one presented by several books). (iii) About "arbitrary depth" type theorems: though we prefer secondary sources (for several reasons, e.g., they help to identify what is more important), the usage of primary sources is not forbidden (furthermore, see the last pillar of [[WP:5p]]: "Wikipedia has policies and guidelines, but they are not carved in stone."). As there are not many secondary sources about the arbitrary depth case, we could use primary sources, as in my view these versions show important new developments. I think that both the L1 version and your theorem is nice and I would keep both of them. What do you think? 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>]] 14:30, 3 July 2020 (UTC)
:::::::: @[[User:Koertefa|''<span style="color:#2F4F4F">'''K'''<span style="color:Teal">œrte</span>'''F'''</span><span style="color:Teal">a</span>'']] Okay, I think we're starting to agree! (i) Constructivity - fair enough; constructivity of proof vs construction in theorem are indeed different points. (ii) Arbitrary depth: okay, let's keep both of them. Although the L1 version actually has an improved Lp version available which I'll state instead. [[User:PatrickKidger|PatrickKidger]] ([[User talk:PatrickKidger|talk]]) 12:43, 6 July 2020 (UTC)
::::::::: OK, sounds good. [[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>]] 19:22, 6 July 2020 (UTC)
== To scientific? Not understandable? ==
No, I think the article is just fine. At least do not abbreviate it. Perhaps this text could be moved more to the end of the article and a more elementary instruction could be written in an introduction. [[Special:Contributions/139.14.20.177|139.14.20.177]] ([[User talk:139.14.20.177|talk]]) 11:54, 25 April 2024 (UTC)
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