Concerns about interpretability, computational resources, and principled inductive priors have motivated efforts to engineer sparse  neural  models for NLP tasks. If sparsity is important for NLP, might well-trained neural models naturally become roughly sparse? Using the Taxi-Euclidean norm to measure sparsity, we find that frequent input words are associated with concentrated or sparse activations, while frequent target words are associated with dispersed activations but concentrated gradients. We find that  gradients associated with function words are more concentrated than the gradients of content words, even controlling for word frequency.
We study the natural emergence of sparsity in the activations and gradients for some layers of a dense LSTM language model, over the course of training.