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I am reading this paper and I came across this. From the 4th paragraph:

We know that element-wise operations imply that $f_{i}$ is purely a function of $w_i$ and $g_i$ is purely a function of $x_i$.

I tried a lot to understand this but I'm unable to understand that. How can we conclude this? Any help is highly appreciated.

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    $\begingroup$ The author is talking about the case where the functions $f_{i}, g_{i}$ are functions only of $w_{i}$, respectively $x_{i}$ $\endgroup$ Jun 5, 2019 at 18:31
  • $\begingroup$ You're saying that he refers to only those cases where $f_i$ and $g_i$ are functions of only $w_i$ and $x_i$ respectively, and only in such cases the diagonal element-wise condition holds true? $\endgroup$ Jun 6, 2019 at 5:06

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