  Second-order semantic parsing with end-to-end mean-field inference has been
shown good performance. In this work we aim to improve this method by modeling
label correlations between adjacent arcs. However, direct modeling leads to
memory explosion because second-order score tensors have sizes of $O(n^3L^2)$
($n$ is the sentence length and $L$ is the number of labels), which is not
affordable. To tackle this computational challenge, we leverage tensor
decomposition techniques, and interestingly, we show that the large
second-order score tensors have no need to be materialized during mean-field
inference, thereby reducing the computational complexity from cubic to
quadratic. We conduct experiments on SemEval 2015 Task 18 English datasets,
showing the effectiveness of modeling label correlations. Our code is publicly
available at https://github.com/sustcsonglin/mean-field-dep-parsing.
