When Every Choice Is Correct: A Causal Study of Numerical Preference in Language Models

Abstract

When a language model chooses a number between 1 and 30, every integer in the range is valid, yet the model can favor particular answers. We use numerical choice to study how preference is processed across layers and tokens. Perturbation probing and gradient attribution nominate neurons for activation interventions. In a selected Qwen3-4B case, a pre-answer edit changes 17 to 15 while both runs first emit 1. After the edit ends, selective cache and attention-output replacements trace part of its continuing influence on the second digit. Replacing one attention head's output or the other heads' outputs jointly produces similar immediate readout contributions; both interventions restore 17 but have different final log-odds effects on 7 versus 5. Holding later multilayer perceptron (MLP) outputs at their values from the edited run without either replacement reduces this effect gap from 0.119 to 0.0025 nat. Later computation therefore changes how similar local contributions affect the continuation. Retrospective estimates across eighteen contexts capture much of the probability movement but miss the selected answer switch. Prompt tests also separate influence from answer changes: one held-out prompt retains influence without switching, and only one of twelve fresh wordings qualifies for the reader/MLP test; there, joint MLP clamping again reduces the gap between the two reader effects while the answer remains 17. These results use numerical choice as a controlled case for studying persistent state and conditional downstream processing; they do not establish the origin or a complete circuit of natural numerical preference.