Talk:Universal approximation theorem: Difference between revisions

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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">—&nbsp;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; furthemorefurthermore they work in the uniformcompact-convergence topology, rather than the L1 topology; furthermore they are narrower. This does still all apply to the ReLU activation function. There has also been another recent paper for general activation functions, but I'm an author on that so I don't know if it's acceptable for me to go around editing Wikipedia pages to mention it... (see also my discussion in 'Out of date', below.) [[Special:Contributions/82.14.199.121|82.14.199.121]] ([[User talk:82.14.199.121|talk]]) 13:40, 7 October 2019 (UTC)

''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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::::::* 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)