Equation 9 · From n-Grams to Reasoning Models: A Technical History of the Language Model
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Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
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Symbol r
r 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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What the article says around this equation
where r is not a learned preference model but a program: a unit test that passes, a numerical answer that matches, a proof that checks. Because r is exact, it cannot be gamed the way a learned reward model can, though it is only available where correctness is mechanically decidable.
Sources cited in the article section
- [20] Chain-of-Thought Prompting Elicits Reasoning in Large Language Models ↗
- [21] Training Verifiers to Solve Math Word Problems ↗
- [22] Tülu 3: Pushing Frontiers in Open Language Model Post-Training ↗
- [23] DeepSeek-R1 Incentivizes Reasoning in LLMs through Reinforcement Learning ↗
These citations give research context. Read each source to check which claims it supports.
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