  Measuring the distance between machine-produced and human language is a
critical open problem. Inspired by empirical findings from psycholinguistics on
the periodicity of entropy in language, we propose FACE, a set of metrics based
on Fourier Analysis of the estimated Cross-Entropy of language, for measuring
the similarity between model-generated and human-written languages. Based on an
open-ended generation task and the experimental data from previous studies, we
find that FACE can effectively identify the human-model gap, scales with model
size, reflects the outcomes of different sampling methods for decoding,
correlates well with other evaluation metrics and with human judgment scores.
