# Why is noise vector represented by letter $z$? [closed]

Most of the notations in Artificial Intelligence are borrowed from the mathematics.

$$x$$ stands for input (vector), $$y$$ stands for output (vector) etc., and the list is long.

But, I am not sure whether $$z$$ has any (widely used) role in mathematics.

Is there any reason behind the usage of letter $$z$$ to represent a noise vector? Or is it just selected randomly without any reason?

• Letter in mathematical discplines are often chosen at random, maybe zzzzz - resembled the noise to the inventor) Aug 1 '21 at 6:56
• Please try to comment whether down-votes reflect the low quality of the question or off-topic-ness of the question or some other. It will be helpful for me and the community. Aug 1 '21 at 11:59

I don't think there's any rationale behind the usage of the letter $$z$$ to denote the noise (which sometimes is also denoted by $$\epsilon$$ in other contexts), apart from the fact that $$x$$ and $$y$$ are already being used and that the letters $$x$$, $$y$$, $$z$$ and $$w$$ are often used to denote variables in mathematics. In particular, in machine learning, $$x$$ and $$y$$ are often used to denote the inputs and outputs (or labels) respectively, while $$w$$ often denotes the parameters (although $$\theta$$ is also used for that).
In other words, it's just a convention (e.g. $$z$$ is also used to denote the hidden variable in the VAE paper). Even if it wasn't and someone used $$z$$ as a mnemonic letter or for some particular reason, I wouldn't lose too much time on this issue, as another author may very well use any other letter to refer to the same concept. It's important to be a bit flexible when it comes to notation in mathematics, otherwise, you may easily get lost.