You Can't Prefer Emotions You Don't Sample: Intensity Undershoot in DPO-Tuned LLMs

Ask a language model to respond "very excitedly," and its output is typically only mildly more energetic. We quantify this effect. We condition an instruction-tuned LLM on a continuous Valence-Arousal (VA) target, where valence measures how pleasant a state is and arousal how activated it is, measure the achieved affect with a frozen regressor, and sweep the requested target from -1 to +1. The response moves far less than asked: the gain, the slope of achieved against requested affect, is only 0.26 for valence and 0.13 for arousal on Llama-3.1-8B, where a faithful controller would score 1. The model systematically undershoots requested emotional intensity, which puts a number on the qualitative observation of Fazzi et al. (2025). Our experiments trace this to the preference-learning pipeline. Training targets from natural corpora such as EmoBank are neutral-heavy, and the sampled candidates themselves rarely reach extreme affect, so Direct Preference Optimization (DPO) is left with no extreme exemplar to prefer. If instead we cover the target space uniformly and sample a hotter, larger candidate pool, valence gain rises from 0.26 to 0.40 +/- 0.02 (3 seeds) and extrapolation error drops, at only a modest in-distribution cost (EmoBank-test VA distance 0.092 to 0.107). The same recipe reproduces on Qwen3-8B (gain_v 0.44, with in-distribution accuracy preserved). Arousal is harder and less reliable: its gain barely moves on average and swings across seeds (0.14 +/- 0.07, against valence's tight +/- 0.02), because raising arousal needs candidates the base model is reluctant to generate. The evidence indicates that faithful intensity is bottlenecked by the extremity of the candidate pool rather than by the conditioning format.