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Equation 25 · Part 2 · The Main Technical Approaches to AI Alignment, Compared

Symbol x

r(x,y)  =  1 ⁣[ y=y⋆(x) ].r(x,y) \;=\; \mathbf{1}\!\left[\, y = y^{\star}(x) \,\right].
xx

What this part means

x is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

x is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

normalizing each sampled response’s reward against the mean and standard deviation of a group of G responses to the same prompt rather than against a separately trained critic network [ 13 ] . Lambert and colleagues, building the fully open Tulu 3 post-training recipe, named the general approach explicitly, describing it as “a novel method we call Reinforcement Learning with Verifiable Rewards,” and used it alongside supervised fine-tuning and preference optimization rather than as a wholesale replacement for either [ 15 ] . The clearest large-scale demonstration is DeepSeek-R1: Guo and colleagues report training a model with reinforcement learning alone against a purely rule-based reward —…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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