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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-->
In the last paragraph of the introduction, the result of n+1 width on continuous convex functions is stated as an "improvement" over the result of n+4 width on Lebesgue-integrable functions. Without additional knowledge of those papers, it's not clear to me why this should be considered an "improvement", since continuous convex functions are a much more restrictive class, and the network width difference is not asymptotically significant.
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