  We formulate a stochastic process, FiLex, as a mathematical model of lexicon
entropy in deep learning-based emergent language systems. Defining a model
mathematically allows it to generate clear predictions which can be directly
and decisively tested. We empirically verify across four different environments
that FiLex predicts the correct correlation between hyperparameters (training
steps, lexicon size, learning rate, rollout buffer size, and Gumbel-Softmax
temperature) and the emergent language's entropy in 20 out of 20
environment-hyperparameter combinations. Furthermore, our experiments reveal
that different environments show diverse relationships between their
hyperparameters and entropy which demonstrates the need for a model which can
make well-defined predictions at a precise level of granularity.
