@InProceedings{goldberger-melamud:2018:C18-1,
  author    = {Goldberger, Jacob  and  Melamud, Oren},
  title     = {Self-Normalization Properties of Language Modeling},
  booktitle = {Proceedings of the 27th International Conference on Computational Linguistics},
  month     = {August},
  year      = {2018},
  address   = {Santa Fe, New Mexico, USA},
  publisher = {Association for Computational Linguistics},
  pages     = {764--773},
  abstract  = {Self-normalizing discriminative models approximate the normalized probability of a class without having to compute the partition function. In the context of language modeling, this property is particularly appealing as it may significantly reduce run-times due to large word vocabularies. In this study, we provide a comprehensive investigation of language modeling self-normalization. First, we theoretically analyze the inherent self-normalization properties of Noise Contrastive Estimation (NCE) language models. Then, we compare them empirically to softmax-based approaches, which are self-normalized using explicit regularization, and suggest a hybrid model with compelling properties. Finally, we uncover a surprising negative correlation between self-normalization and perplexity across the board, as well as some regularity in the observed errors, which may potentially be used for improving self-normalization algorithms in the future.},
  url       = {http://www.aclweb.org/anthology/C18-1065}
}