You seem to think backtracking cannot occur within (?>PAT). That's not the case at all.
The purpose of (?>PAT) is to prevent the regex engine from trying to get PAT to match something else once it has already matched something. In short, backtracking through (?>PAT) causes it to fail.
You want
/^\d+ _\d+ (?> (?:_\d+)? ) \w+ $/x
which can also be written as
/^\d+ _\d+ (?:_\d+)?+ \w+ $/x
For "1_0_1" =~ /^\d+ _\d+ (?> (?:_\d+)? ) \w+ $/x, everything is straightforward until /\w+/ fails to match. At that point, the regex engine starts to backtrack.
- Backtracking through causes it (?>...) fail (as always).
- Backtracking through causes it \d+ fail (since it previously only matched only one digit).
- Backtracking through causes it _ fail (as always).
- Backtracking through causes it \d+ fail (since it previously only matched only one digit).
- Backtracking through causes it ^ fail (as always).
- The match fails.
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