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What is the meaning of putting uniform distribution inside log? See page 5 of this paper (Corentlin et al.)

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To make it more clearer, within my knowledge, I think I should put a single value inside log(). I have no idea what is the meaning that put a distribution inside. Does it result in another distribution? It's strange to me because I think the author want to get a single value.

It seems like this is really an easy question but I just can't figure it out, and I keep finding log-uniform on internet, which I believe it's not.
Thanks in advance!

References

Corentin Tallec, Yann Ollivier. Can Recurrent Neural Network Warp Time? ICLR 2018

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    $\begingroup$ 1. This is explicitly discussed in the first sentence on page 5. 2. Please give a full reference and some context for the problem being discussed, not just a link. $\endgroup$
    – Glen_b
    Commented May 14, 2018 at 4:53
  • $\begingroup$ @Glen_b I don't see how the first sentence on page 5, "Values of..." would explicitly discuss the meaning of this notation. But I agree a full reference to the paper is appropriate $\endgroup$
    – Juho Kokkala
    Commented May 14, 2018 at 6:11
  • $\begingroup$ Sorry I'm new to this community. I have edited my post, please check. $\endgroup$
    – B.H. Chiang
    Commented May 14, 2018 at 8:17
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    $\begingroup$ Why do you believe it's not log uniform? $\endgroup$
    – Peter Flom
    Commented May 14, 2018 at 12:13
  • $\begingroup$ @Juho It explains why there's a log in the expression in the question. $\endgroup$
    – Glen_b
    Commented May 14, 2018 at 17:46

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This is somewhat informal notation, but it cannot have any other meaning than a random variable which is minus the log of a uniform random variable.

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