When Do Repetition Loops Lock? Truncation Sampling, Bounded Penalties, and a Blind Spot in DRY

Overview & Synopsis

Language models sometimes repeat verbatim until the generation limit. We study the exit rather than the entrance: given that a span has already been repeated $n$ times, when is escape still possible? Along the loop the context is deterministic, so loop survival under any sampler can be computed exactly from one forward pass. Pure sampling leaves a positive escape probability at every step; top-$p$ with threshold $π>1/2$ locks a position exactly when the continuation probability reaches $π$. A bounded penalty can leave a position locked; a penalty that outgrows the model's preference for the loop over unseen tokens guarantees escape under top-$p$. The same analysis predicts a blind spot in the widely deployed DRY sampler: its sequence breakers cap the penalty at $λb^{g-1-a}$ for loops whose longest breaker-free run has $g$ tokens. On eleven open models, 66\% of locked units with $g=6$ stay locked under DRY and 1\% with $g=8$. In free generation with llama.cpp, all 109 loops that survive DRY have $g\le 7$. We propose DRY-C, which adds a term that grows exponentially with the number of verbatim recurrences, up to its look-back window. With it, none of 720 structured-output generations looped to the length limit, and task completion stayed close to DRY's.