Equation 1 · How Constitutional AI Actually Constrains a Model's Behavior
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Crucially, this AI-generated harmlessness comparison data did not replace human comparison data outright; it was combined with it. The paper reports 135,296 human helpfulness comparisons and 182,831 constitutionally generated harmlessness comparisons feeding one preference model, trained on the union of both, in the authors’ words: “we use human labels for helpfulness, but only AI labels for harmlessness.” A single Bradley-Terry-style preference loss is fit across both sources at once. Writing for the human comparison set, for the AI-generated set, for the reward model, x for a prompt, and , for the winning and losing response in a pair, the objective is
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