Task: Question Generation
Input (English): Since labels are unknown on INLINEFORM1 , EGL computes the expectation of the gradient norm over all possible labelings. BIBREF3 interprets EGL as “expected model change”. In the following section, we formalize the intuition for EGL and show that it follows naturally from reducing the variance of an estimator. Eq. ( EQREF7 ) indicates that to reduce INLINEFORM0 on test data, we need to minimize the expected variance INLINEFORM1 over the test set. A practical issue is that we do not know INLINEFORM0 in advance. We could instead substitute an estimate INLINEFORM1 from a pre-trained model, where it is reasonable to assume the INLINEFORM2 to be close to the true INLINEFORM3 . The batch selection then works by taking the samples that have largest gradient norms, DISPLAYFORM0

For RNNs, the gradients for each potential label can be obtained by back-propagation. Another practical issue is that EGL marginalizes over all possible labelings, but in speech recognition, the number of labelings scales exponentially in the number of timesteps. Therefore, we only marginalize over the INLINEFORM0 most probable labelings. They are obtained by beam search decoding, as in BIBREF7 . The EGL method in BIBREF3 is almost the same as Eq. ( EQREF8 ), except the gradient's norm is not squared in BIBREF3 .
Output (English): How do they calculate variance from the model outputs?