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A Proofs

Neural Information Processing Systems

In this section, we give full proofs of the two main theorems in the paper. 's invertibility and equality 9 follows from Definition 5. Then for By Jensen's inequality, we have: ξ In this section, we give more details of the algorithms we used in the paper. For each i { 1, 2,...,m }, there are n Our code is written with PyTorch. Section 4 and we choose our hyperparameters by the validation performance on the dev sets. The majority of the MNLI corpus is released under the OANC's license, and CMLE method (see Equation 4).