The key difference between the two expressions is that f I scores the start and the end of each span independently, while f J scores them jointly.
we define f J : R h → R and f I : R h → R to be transformations of the final token representations computed by a BERT model: Here h is the hidden representation dimension, (s, e) = a is the answer span, BERT(t)[i] is the BERT representation of the i'th token in token sequence t. MLP J is a multi-layer perceptron with a single hidden layer, and AFF I is an affine transformation.