# with components pa = P r(a|s) (Math)

#### NewAmerica

##### Senior Member
Is "|" in "P r(a|s) " read as vertical line?

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Instead of a handcrafted evaluation function and move ordering heuristics, AlphaZero utilises a deep neural network (p, v) = fθ(s) with parameters θ. This neural network takes the board position s as an input and outputs a vector of move probabilities p with components pa = Pr(a|s) for each action a, and a scalar value v estimating the expected outcome z from position s, v ≈ E[z|s].

-arXiv

Source

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##### Senior Member
To my knowledge, the keystroke is called a pipe. It may be called something else when it's in a math context.

#### dojibear

##### Senior Member
I would not attempt to "read" the equation (say it verbally, and assume the listener can correctly write it down).

In software and some math, this vertical line is an "or". Copyright mentions "a pipe", which is a unix command line concept that uses the vertical line. (It may also work in the command lines of Windows and/or Mac O/S: I don't know).

But I do not know this notation. It doesn't match any that I've used in software (but I've never worked with neural nets). Why is there a space between P and r, and what does that space mean? What does the vertical line mean? I'm fairly sure it isn't "or" or a "pipe" in this formula.

#### JulianStuart

##### Senior Member
It seems clearly a specific notation for neural network specialists and not intended for those without training in such a field. They would also know how to say it out loud if necessary to explain to beginnners Are you studying the maths associated with this paper or are you just curious in general about the | character?

#### NewAmerica

##### Senior Member
Thank you.

Why is there a space between P and r, and what does that space mean? What does the vertical line mean? I'm fairly sure it isn't "or" or a "pipe" in this formula.
P r should have been Pr. Our forum editor mistakenly put space there.

It seems clearly a specific notation for neural network specialists and not intended for those without training in such a field. They would also know how to say it out loud if necessary to explain to beginnners Are you studying the maths associated with this paper or are you just curious in general about the | character?
The paper is apparently a grand landmark in AI field. A "superman" paper. That is why I am so interested in it.

#### manfy

##### Senior Member
Since you're talking about a probability calculation, you'd probably read Pr(a|s) as "the probability of a given s".

Wiki knows many other possibilities, though! See <here>.

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