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Equation 4 · Part 1 · Training on Your Own Output: Synthetic Data and What It Does to a Distribution

Symbol hatp_k+1

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),
p^k+1\hat{p}_{k+1}

What this part means

the classical collapse setting.

Its job in the formula

hatpkp_k+1 is part of the quantity the equation computes from the expression on the right.

Where the article explains it

The classical collapse setting is

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

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 article section

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