  The performance of deep learning in natural language processing has been
spectacular, but the reasons for this success remain unclear because of the
inherent complexity of deep learning. This paper provides empirical evidence of
its effectiveness and of a limitation of neural networks for language
engineering. Precisely, we demonstrate that a neural language model based on
long short-term memory (LSTM) effectively reproduces Zipf's law and Heaps' law,
two representative statistical properties underlying natural language. We
discuss the quality of reproducibility and the emergence of Zipf's law and
Heaps' law as training progresses. We also point out that the neural language
model has a limitation in reproducing long-range correlation, another
statistical property of natural language. This understanding could provide a
direction for improving the architectures of neural networks.
