Task: Question Answering
Input (English): The goal of an language model is to assign meaningful probabilities to a sequence of words. Given a set of tokens $\mathbf {X}=(x_1,....,x_T)$, where $T$ is the length of a sequence, our task is to estimate the joint conditional probability $P(\mathbf {X})$ which is

were $(x_{1}, \ldots , x_{i-1})$ is the context. An Intrinsic evaluation of the performance of Language Models is perplexity (PPL) which is defined as the inverse probability of the set of the tokens and taking the $T^{th}$ root were $T$ is the number of tokens We propose an approximation of the joint probability as,

This type of approximations has been previously explored with Bi-directional RNN LM's BIBREF9 but not for deep transformer models. We therefore, define a pseudo-perplexity score from the above approximated joint probability. 
 Question: How is pseudo-perplexity defined?
Output (English): Answer with content missing: (formulas in selection): Pseudo-perplexity is perplexity where conditional joint probability is approximated.