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Equation 8 · Part 3 · Training on Your Own Output: Synthetic Data and What It Does to a Distribution

Symbol D_0

p^k+1=F(D0∪S1∪⋯∪Sk),\hat{p}_{k+1} = \mathcal{F}\left( D_0 \cup S_1 \cup \cdots \cup S_k \right),
D0D_0

What this part means

the original real corpus and SjS_j the synthetic output of generation j.

Its job in the formula

D0D_0 is an input to the expression that computes the quantity on the left.

Where the article explains it

where D0D_0 is the original real corpus and SjS_j the synthetic output of generation j .

The passage around this formula

Change one term and the analysis changes with it. Consider instead p^k+1=F(D0∪S1∪⋯∪Sk)\hat{p}_{k+1} = \mathcal{F}\left( D_0 \cup S_1 \cup \cdots \cup S_k \right). where D0D_0 is the original real corpus and SjS_j 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…

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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

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