Before and After Temperature: A Distributional View of Creative LLM Generation

Reference-free evaluation of large language model (LLM) creativity relies on perplexity, entropy, and top-1 margin. We show that a much stronger signal lives one step earlier in the pipeline: in how sampling temperature reshapes the model's token distribution before the next token is drawn. On Llama-3.1-8B-Instruct generations of 500 open-ended creative prompts at T \in {0.3, 0.8, 1.5}, a single per-token feature derived from this reshaping predicts the within-prompt creativity rank at Spearman ρ{=}0.918 against an averaged gpt-4o,/,gemini-2.5-pro judge (n{=}500) and ρ{=}0.870 against a three-rater human-majority ranking (n{=}150). Each of four standard reference-free baselines (self-perplexity, mean predictive entropy, top-1 margin, gzip compression ratio) tops out at |ρ|!\approx!0.76 on both ground truths: a gap of +0.165 on averaged-LLM and +0.110 on human-majority, both far larger than the spread among the baselines themselves. The two ground-truth panels agree with each other at ρ{=}0.83, above the inter-human ceiling of ρ{=}0.77, so the comparison is not bottlenecked by judge noise. Mechanistically, the win comes from a sharp distributional signature of the incoherence regime: at T{=}1.5 the cumulative-mass width n_{95}(q) inflates from \sim!1 to {\sim}!131 tokens and post-temperature mass leaks off the pre-temperature top-90% plausible set by about 13 percentage points. The per-token aggregates do not separate T{=}0.8 from T{=}0.3; discriminating the two coherent regimes is left to sequence-level features.