Accuracy vs. Perplexity

If model A has higher accuracy than model B, does it necessarily imply
perplexity(A) < perplexity(B)?

Jason's reply:

No, that is not implied.
Accuracy = how correct is the highest-probability hypothesis?
Perplexity = how probable is the correct hypothesis?
(or more generally, how probable is the observed data?)

So they are really measuring different things.
Accuracy is what you really care about, in a sense,
but (1) it is only defined if you have supervised data,
(2) it requires an evaluation method for measuring degree
of correctness, (3) it is usually not a continuous function
of the parameters (since an epsilon change in the parameters
may not change which hypothesis has the highest probability)
and is therefore hard to optimize.

I usually recommend reporting both, which has become
the convention in speech recognition, where people report
WER (word error rate) and perplexity.