  Neural Network based models have been state-of-the-art models for various
Natural Language Processing tasks, however, the input and output dimension
problem in the networks has still not been fully resolved, especially in text
generation tasks (e.g. Machine Translation, Text Summarization), in which input
and output both have huge sizes of vocabularies. Therefore, input-output
embedding weight sharing has been introduced and adopted widely, which remains
to be improved. Based on linear algebra and statistical theories, this paper
locates the shortcoming of existed input-output embedding weight sharing
method, then raises methods for improving input-output weight shared embedding,
among which methods of normalization of embedding weight matrices show best
performance. These methods are nearly computational cost-free, can get combined
with other embedding techniques, and show good effectiveness when applied on
state-of-the-art Neural Network models. For Transformer-big models, the
normalization techniques can get at best 0.6 BLEU improvement compared to the
original version of model on WMT'16 En-De dataset, and similar BLEU
improvements on IWSLT 14' datasets. For DynamicConv models, 0.5 BLEU
improvement can be attained on WMT'16 En-De dataset, and 0.41 BLEU improvement
on IWSLT 14' De-En translation task is achieved.
