Gauge dependence and structured-output corruption in sign-branched repetition penalties: measurements across models, inference stacks, and alternative repetition controls
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, and the sign-branch reads that arbitrary point. The sign-branch is itself the accepted fix for an earlier bug, so the accepted fix branches on a quantity the training objective leaves unconstrained. 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, where 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%. In our measurements, applying the penalty to normalized log-probabilities instead of raw logits removes both effects. HuggingFace already ships that operator (LogitNormalization); today it is off by default and applied after the penalty. This note gives the mechanism, the measurements (five models up to 7B, base and RLHF, on WikiText-103 prefixes; two code models on HumanEval and JSONSchemaBench; both effects replicated inside vLLM and llama$.$cpp through their own samplers on the same inputs), and the normalized variant.