Equation 10 · Part 1 · Training on Your Own Output: Synthetic Data and What It Does to a Distribution
Symbol S_j
What this part means
the synthetic output of generation j.
Its job in the formula
is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol S_j→Article meaning
Where the article explains it
where is the original real corpus and the synthetic output of generation j .
The passage around this formula
where is the original real corpus and the synthetic output of generation j . Gerstgrasser and colleagues make exactly this substitution and report that while replacing real data with each generation’s synthetic data does tend toward collapse, accumulating successive generations alongside the original real data avoids it — across transformers, diffusion models and variational autoencoders — and they prove that under accumulation the test error has a finite upper bound independent of the number of iterations [ 2 ] . The accumulating case is also the more accurate description of the actual web, which does not delete last year’s pages when this year’s are published.
Learn the underlying idea
A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.