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

Mathematically Modeling the Lexicon Entropy of Emergent Language