Suppose we are given a specific language model such as GPT-2 BIBREF6, GROVER BIBREF8, or CTRL BIBREF7, and it is characterized in terms of estimates of either cross-entropy $H(P,Q)$ or perplexity $\mathrm {PPL}(P,Q)$.

We can see directly that the Neyman-Pearson error of detection in the case of i.i.d. tokens is:

and similar results hold for ergodic observations.

Since we think of $H(P)$ as a constant, we observe that the error exponent for the decision problem is precisely an affine shift of the cross-entropy. Outputs from models that are better in the sense of cross-entropy or perplexity are harder to distinguish from authentic text.

Thus we see that intuitive measures of generative text quality match a formal operational measure of indistinguishability that comes from the hypothesis testing limit. 
 Question: Which language models generate text that can be easier to classify as genuine or generated?
Outputs from models that are better in the sense of cross-entropy or perplexity are harder to distinguish from authentic text.