Equation 7 · Part 2 · How Training Data and Synthetic Data Actually Work
addition
addition
What this part means
Add the term after the plus sign to the term or group before it.
Its job in the formula
Add the term after the plus sign to the term or group before it.
Full expression→addition→Article meaning
The passage around this formula
The word “irreversible” is precise and load-bearing: it does not mean the process is fast, or that any synthetic data at all causes it, or that mixing synthetic data with real data necessarily triggers it. It means that once the tails of the distribution are lost through repeated recursive resampling without fresh real data anchoring each generation, that specific information cannot be recovered from later generations of the same recursive process, because it never encoded a copy of those tails anywhere in the chain. This is the load-bearing distinction between the phi-model result and the collapse result, and conflating them is the most common misreading of both papers. Phi-1’s synthetic…
Learn the underlying idea
Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.
Open the illustrated addition and subtraction in an equation guide →
Sources cited in the surrounding passage
- [4] Textbooks Are All You Need ↗
- [1] The Curse of Recursion: Training on Generated Data Makes Models Forget ↗
These citations provide research context; check each source for the exact claim it supports.