Does Slightly Mean Somewhat? Measuring Vague Intensity Words in LLM Numeric Actions

Quantities with measurement units, such as 110 cm and 1.2 m, require language models (LMs) to combine a numeral with a symbolic unit scale. Here, we study how LMs compare such quantities in controlled settings spanning several unit systems. We find that accuracy degrades near the comparison boundary, where small changes in value determine the correct answer. The resulting errors are systematic: linear surrogate models predict LM preferences from numerical-difference and unit-scale-difference cues, and causal interventions on subspaces aligned with these variables shift model's output. The results suggest that LMs compare quantities through a bag of heuristics over numerals and units, rather than first converting both expressions to an exact shared-scale representation.

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.

When a language model must choose one answer from a large space of equally valid options, a format clause -- "Reply with JSON only" -- changes which answer it chooses. We re-run the One-Word Census (arXiv:2607.12796): 31 wide-answer-space category prompts asked of 44 models, now with the reply requested in JSON -- no schema enforcement, no constrained decoding, only the request. Convergence deepens sharply: on the unconstrained "Pick a word" prompt the modal answer rises from 41% to 64% of the pool and distinct answers fall from 52 to 36; mean answer-choice surprisal drops from 1.80 to 1.58 bits. The tax is progressive: six of 44 models move individually (BH-FDR q=.10), all toward the mode, led by the most distinctive models, while the conformist floor is immobile. It is a sharpener, not a re-indexer -- the plain-chat modal answer survives in 28 of 31 categories. Defaults are register-indexed: a within-run re-sample (n=20) finds JSON shifts 53% of a model's stable chat defaults, mostly back to the crowd, and installs defaults absent from chat (Claude Fable 5 answers "cerulean" for colour 0% of the time in chat, 100% in JSON). Full-battery controls reveal a register gradient: compression is significant and specific to the answer-delivery formats models are trained to speak (JSON -0.22 bits, p=.0002; XML -0.19, p=.002), absent for YAML and CSV, and reversed for an arbitrary bracket wrapper (+0.13, p=.009) -- weighing the mechanism toward tool-use post-training. Enforcing the schema at the decoder (response_format) compresses no further than the request (-0.03 bits): the collapse lives in the model's response to the register, not the decoder. Structured output is how software consumes language models, and that surface is served by a measurably more homogeneous model than the chat surface on which models are evaluated, compared, and chosen.