Equation 7 · Part 1 · How Constitutional AI Actually Constrains a Model's Behavior
Symbol x
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x is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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The passage around this formula
Nothing in that loss distinguishes where a pair came from; a human-labeled winner and an AI-labeled winner are interchangeable once written down as (x, , ) . That is the precise, narrow sense in which Constitutional AI “differs mechanically from plain RLHF”: it changes the labeling function for one half of one dataset, not the loss, not the optimizer, not the use of a KL penalty against the supervised policy. For the soft-labeled AI comparisons specifically, where the feedback model outputs a probability p of preferring response over rather than a hard choice, the corresponding cross-entropy term is
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