For that one can use so called "Dynamic Filter Option" (these can be defined/created too, but quite a few exist OOB).

It looks like this:

This will make the system "resolve" the operand (Me) before applying the filter, so it becomes Caller is Developer.

If we copy the query:

 it will look like this:

caller_idDYNAMIC90d1921e5f510100a9ad2572f2b477fe

90d1921e5f510100a9ad2572f2b477fe is the unique id of the Dynamic Filter Option:

This is an OOB Dynamic Filter Option, so it will be there in all instances and can be used; thus you can set your filter like this:

active=true^caller_idDYNAMIC90d1921e5f510100a9ad2572f2b477fe

Which can be obtained by copying the filter defined below: