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Equation 25 · Part 5 · The Main Technical Approaches to AI Alignment, Compared

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.