Perplexity and cross-entropy for n-gram models

Trying to understand the relationship between cross-entropy and perplexity. In general for a model M, Perplexity(M)=2^entropy(M) . Does this relationship hold for all different n-grams, i.e. unigram, bigram etc.?

• That's actually the definition of perplexity; the $\sqrt[N]{\Pi^N_{i=1} \frac{1}{P(w_i|w_1, ... w_{i-1})}}$ thing is derived from it ;) Jun 19 '17 at 6:32