ambrus taught me a good mnenonic - the negated comparison for the regex binding operator is !~, which has the same order as !=, and thus, the regex binding operator must be =~.

I use the same mnemonic but word it a bit differently: I tend to translate $a == $b to "a is b", so I translate $a =~ /Pattern/ as "a is like Pattern", and since ! is traditionally "not" I translate $a !~/Pattern/ as "a not like Pattern".

Thus the "=~" operator to me is the "is like" operator and the "!~" operator is the "not like" operator.