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Understanding geometric properties of natural language processing models'latent spaces allows the manipulation of these properties for improvedperformance on downstream tasks. One such property is the amount of data spreadin a model's latent space, or how fully the available latent space is beingused. In this work, we define data spread and demonstrate that the commonlyused measures of data spread, Average Cosine Similarity and a partitionfunction min/max ratio I(V), do not provide reliable metrics to compare the useof latent space across models. We propose and examine eight alternativemeasures of data spread, all but one of which improve over these currentmetrics when applied to seven synthetic data distributions. Of our proposedmeasures, we recommend one principal component-based measure and oneentropy-based measure that provide reliable, relative measures of spread andcan be used to compare models of different sizes and dimensionalities.

Reliable Measures of Spread in High Dimensional Latent Spaces