[Submitted on 26 Oct 2026]
Title:3, 7, 14, 17, 42: Instruction Tuning Installs and Sharpens Number-Choice Heuristics in Language Models
View a PDF of the paper titled 3, 7, 14, 17, 42: Instruction Tuning Installs and Sharpens Number-Choice Heuristics in Language Models, by Samar Ansari
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Abstract:We measure, without sampling error, the probability a language model assigns to each integer from 1 to N when asked for a random number. For a fixed prompt the model defines one probability vector, which we compute by summing over each integer's scored spellings rather than estimate by sampling, removing the noise that limits earlier studies [1, 4]. We evaluate 18 open-weight model lines at five ranges up to N = 100, under 29 decoding configurations, on two inference stacks; 15 of them have matched base and instruction-tuned checkpoints that both give usable answers. Instruction tuning makes the distribution less uniform in all 15 pairs. It installs one heuristic, round-number avoidance, and sharpens another, endpoint avoidance. Base checkpoints do not avoid round numbers once the endpoints are removed from those sets; tuned checkpoints avoid them, multiples of 10 almost completely. Base checkpoints return the endpoints 1 and N at 0.30 to 0.60 of the interior rate; tuned checkpoints almost never return them. A preference for odd numbers is consistent across tuned checkpoints only at N = 100, where base checkpoints also show it weakly. Endpoint avoidance and the odd preference fit the account Kubovy and Psotka [6] proposed for human number choice; round-number avoidance is not part of that account, and the midpoint avoidance it predicts is essentially absent, with one slight exception at N = 100. Tuning does not install a new favourite integer shared across models: above N = 10 no modal integer is shared by more than 42 percent of tuned conditions, and P (17) rises in 10 of 15 pairs and falls in 5. The concentration is present in the model's own distribution: at temperature 1.0, nucleus truncation at top-p 0.95 adds a median of 0.035 to the total variation distance.
Subjects:
Computation and Language (cs.CL)
Cite as: arXiv:2610.36178 [cs.CL]
(or arXiv:2610.36178v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2610.36178
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Mohammad Samar Ansari Ph.D. [view email] [v1] Mon, 26 Oct 2026 19:12:46 UTC (132 KB)
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