Gauge dependence and structured-output corruption in sign-branched repetition penalties: measurements across models, inference stacks, and alternative repetition controls

Abstract

The multiplicative repetition penalty shipped across the LLM inference ecosystem (HuggingFace, vLLM, llama.cpp, and a dozen further engines) branches on the sign of each raw logit (divide positives by $\theta$, multiply negatives). But the softmax is unchanged by adding a constant to every logit, so a model’s logit zero-point is arbitrary (a gauge choice), and the sign-branch reads it. Two measurable consequences follow. (1) The penalty is not well-defined: re-centring a model’s logits by a constant is a provable no-op at $\theta=1$, yet at a routine $\theta=1.3$ it changes 58–96% of greedy tokens, while subtractive and normalized penalties change none; real checkpoints sit at widely different zero-points, so a fixed repetition_penalty is a different operation on every model. (2) It corrupts structured output: on 200 real-world JSON schemas, $\theta=1.3$ drops the rate of valid, schema-conformant output from 97% to 23%. Applying the penalty to normalized log-probabilities instead of raw logits removes the gauge dependence by construction; HuggingFace’s beam search has applied its processor chain, penalty included, to log-probabilities since at least v4.0.0, so repetition_penalty already names two different operators depending on decoding strategy. Because equal $\theta$ is not equal strength across the two operators, we also compare them at matched suppression, calibrated per model by search: there the normalized operator is statistically no worse on any quality metric measured, but on four of seven models it cannot match the raw operator’s suppression at $\theta \geq 1.15$, and on six of seven at $\theta=1.3$, the setting where the corruption was measured. This note gives the mechanism, the measurements (five models up to 7B; two code models; both effects replicated inside vLLM and llama.cpp through their own samplers), the per-model calibration map, and the normalized variant.