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.

Parsing sentences into syntax trees can benefit downstream applications inNLP.

A fundamental problem in deep neural networks is toverify or certify that a trained network is robust, i.e. not susceptible to adversarial attacks [11, 29, 39].

Instead, we seek to learn a fair distribution overthearms. Drawing onalong lineofresearch ineconomics and computer science, we use theNash social welfareas our notion of fairness.

BLUE (Biomedical Language Understanding Evaluation) is abenchmarkfor 10 datasetsrepresenting 5 tasks [34]. BLURB (Biomedical Language Understanding and Reasoning Benchmark) includes 13 datasetsand 7 tasks [19].