3, 7, 14, 17, 42: Instruction Tuning Installs and Sharpens Number-Choice Heuristics in Language Models

Instruction tuning makes language models less uniform in the integers they assign probability to when asked for a random number, according to an arXiv paper (2610.36178v1) that computed exact probability vectors for 18 open-weight model lines at five ranges up to N = 100. Across the 15 model pairs with matched base and instruction-tuned checkpoints, tuning installed round-number avoidance and sharpened endpoint avoidance: base checkpoints returned 1 and N at 0.30 to 0.60 of the interior rate, while tuned checkpoints almost never returned them and avoided multiples of 10 almost completely. No single favorite integer was shared across models above N = 10 by more than 42 percent of tuned conditions, and P(17) rose in 10 of 15 pairs and fell in 5.

arXiv:2610.36178v1 Announce Type: new 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.