Equation 8 · Part 5 · Comparing the Main Approaches to Training Data and Synthetic Data
fraction
fraction
What this part means
Divide the expression above the line by the one below it.
Its job in the formula
The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.
Full expression→fraction→Article meaning
The passage around this formula
Rejection sampling generates multiple candidate completions per prompt from a model and keeps only the ones a separate scoring step accepts, using the survivors as supervised fine-tuning data. Llama 2’s RLHF pipeline used exactly this for its first four rounds, generating candidates from the 70-billion-parameter model, scoring them against a trained reward model, and only introducing proximal policy optimisation as a second mechanism in later rounds once the returns from sampling alone began to taper [ 6 ] . A second, independent demonstration in mathematical reasoning makes the mechanism even more explicit: rejection sampling fine-tuning collects correct reasoning paths directly from a…
Learn the underlying idea
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
Open the illustrated fractions: division written vertically guide →
Sources cited in the surrounding passage
- [6] Llama 2: Open Foundation and Fine-Tuned Chat Models ↗
- [7] Scaling Relationship on Learning Mathematical Reasoning with Large Language Models ↗
These citations provide research context; check each source for the exact claim it supports.