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Equation 4 · Part 6 · Training on Your Own Output: Synthetic Data and What It Does to a Distribution

=

p^k+1=F(X1,…,Xn∼p^k),\hat{p}_{k+1} = \mathcal{F}\left( X_1, \ldots, X_n \sim \hat{p}_k \right),
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Let p^k\hat{p}_k be the model fitted at generation k , and F\mathcal{F} the fitting procedure. The classical collapse setting is p^k+1=F(X1,…,Xn∼p^k)\hat{p}_{k+1} = \mathcal{F}\left( X_1, \ldots, X_n \sim \hat{p}_k \right). in which generation k+1 sees n samples drawn from its immediate predecessor and nothing else . The original data are gone. No filter selects among the samples. The lineage is single. Under those conditions, degradation compounds because there is no channel by which an error introduced at generation k can ever be corrected.

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.