Thismakesinferenceveryfast,andmaynot even need to use all input featuresto make a prediction (with axis-aligned trees).

Conversely,ifsuch xandy donot exist,wesayT doesnotcontainunarychains. Then we present Algorithm 1 for computing oracle actions. Given a constituency treeT without unary chains, it recursively finds and undoes the last action untilT becomes empty_tree. Let T be a constituency tree for a sentence of length n. And this sequence of actions can be computed via Algorithm1. When n > 0, it is sufficient to proveT0 is a valid constituency tree without unary chains for a sentence oflengthn 1. Weproceed byenumerating allpossible execution traces inlast_action.

In this paper, we focus on computing an NE that optimizes a given objective function.

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