Equation 11 · Part 1 · Training on Your Own Output: Synthetic Data and What It Does to a Distribution
Symbol j
What this part means
j is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Its job in the formula
j 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 j→Article meaning
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 variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.