The Branching Factor of a language is the number of possible next words that can follow any word. Perplexity can be thought of as the Weighted Average Branching Factor of a language.

University of Michigan - Ann Arbor

Using perplexity is a method of measuring quality of a language model. Perplexity of a model θ on an unseen test set is the inverse probability assigned by θ to the test set, which is normalized by the test set length.

Minimizing perplexity is equivalent to maximizing the test set probability in the language model.

Perplexity

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

For a test set $W = w_1…w_n$, its perplexity is
$$PP(W) = \left(\prod_{i=1}^{N}\frac{1}{P(w_i|w_1...w_{i-1})}\right)^{\frac{1}{N}}$$

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