Equation 10 · From n-Grams to Reasoning Models: A Technical History of the Language Model
What does this equation mean?
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.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
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.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
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.
Return to From n-Grams to Reasoning Models: A Technical History of the Language Model